On the Role of Polymer Viscoelasticity in Enhanced Oil Recovery: Extensive Laboratory Data and Review

Article On the Role of Polymer Viscoelasticity in Enhanced Oil Recovery: Extensive Laboratory Data and Review

Alexander Rock, Rafael E. Hincapie * , Muhammad Tahir , Nils Langanke and Leonhard Ganzer

Institute of Subsurface Energy Systems, Clausthal University of Technology, 38678 Clausthal-Zellerfeld, Germany; [email protected] (A.R.); [email protected] (M.T.); [email protected] (N.L.); [email protected] (L.G.) * Correspondence: [email protected]; Tel.: +49-176-3049-0541

Received: 5 September 2020; Accepted: 28 September 2020; Published: 3 October 2020

Abstract: Polymer flooding most commonly uses partially hydrolyzed polyacrylamides (HPAM) injected to increase the declining oil production from mature fields. Apart from the improved mobility ratio, also the viscoelasticity-associated flow effects yield additional oil recovery. Viscoelasticity is defined as the ability of particular polymer solutions to behave as a solid and liquid simultaneously if certain flow conditions, e.g., shear rates, are present. The viscoelasticity related flow phenomena as well as their recovery mechanisms are not fully understood and, hence, require additional and more advanced research. Whereas literature reasonably agreed on the presence of these viscoelastic flow effects in porous media, there is a significant lack and discord regarding the viscoelasticity effects in oil recovery. This work combines the information encountered in the literature, private reports and field applications. Self-gathered laboratory data is used in this work to support or refuse observations. An extensive review is generated by combining experimental observations and field applications with critical insights of the authors. The focus of the work is to understand and clarify the claims associated with polymer viscoelasticity in oil recovery by improvement of sweep efficiency, oil ganglia mobilization by flow instabilities, among others.

Keywords: hydrolyzed polyacrylamides; viscoelasticity; oil recovery

1. Introduction

1.1. Overview of Polymer-Enhanced Oil Recovery Although oil production is currently assumed to be higher than the actual demand, the future of oil and gas production will have to tackle severe challenges: fewer new fields are found and major producing fields show declining production. Most of the latter fields traversed all three production phases of an oil reservoir. A primary recovery phase using the natural energy present in the reservoir can reach recovery factors (RF) of up to 30% [1]. A secondary production phase using artificial methods such as pressure support by water flooding or the application of pumps can yield RFs of approximately 50–60% [1,2]. The last phase of recovery—the tertiary recovery phase enhanced oil recovery (EOR) methods—is applied in order to achieve RFs of up to 80% [3,4]. Currently, the modern oil and gas industry possess several EOR options that could be applied, such as thermal methods (often for heavy oil recovery) by introducing additional heat into the reservoir [5], miscible processes with injection of CO2 for example [6] and chemical applications such as polymer flooding, surfactant flooding and combined processes, e.g., alkaline-surfactant-polymer flooding [7]. In a more specific sense, polymer flooding has proven to be an excellent process economically speaking as a well-recognized and widely used chemical EOR method. This is mainly due to the

Polymers 2020, 12, 2276; doi:10.3390/polym12102276 www.mdpi.com/journal/polymers Polymers 2020, 12, 2276 2 of 43 large number of advanced and extensive experimental investigations (e.g., [2,8–15] as well as due its success in field applications such as the Daqing oil field in China [16]. The remarkable potential of polymer EOR is additionally underlined by Sheng et al. [17] who analyzed 733 polymer flooding projects around the world. The compilation shows that the oil recovery utilizing polymer injection results in a 6.7% higher recovery than using conventional water flooding. Several mechanisms are being used to explain the oil recovery due to polymer process application in reservoirs. Although, there appears to be a sort of consensus, researchers keep on searching for clear explanations and answers. The mechanisms behind the observed recovery factors that can be found in the literature are manifold but can be grouped as follow in Table1.

Table 1. Overview of the mechanism reported that could explain polymer enhanced oil recovery (EOR) applications.

Mechanism Reference Sheng et al. [17], Sheng [14], 1 Relative Permeability Reduction Huh and Pope [9], Abidin et al. [18] Sheng et al. [17], Sheng [14], Clarke et al. [2], 2 Viscous Fingering Reduction Dong et al. [16], Abdul Hamid and Muggeridge [19], Tahir et al. [20] Enhanced Flow between Vertical, 3 Sheng et al. [17], Sorbie [21] Heterogeneous Layers 4 Pull-Out in Dead End Pores Luo et al. [22], Yin et al. [23] Stripping from Oil-Wet Rock 5 Wang [24] Surface Rock et al. [11], Hincapie [8], Howe et al. [25], 6 Shear Thickening Clarke et al. [2], Azad and Trivedi [26–28] Hincapie et al. [29], Rock et al. [30], Groisman 7 Elastic Turbulence and Steinberg [31]

Although polymer flooding offers an extensive variety of recovery mechanisms and shows remarkable success in field applications, it comes with some considerable technical and economic challenges. First of all, polymer flooding projects require significant planning and testing for successful field implementation, e.g., laboratory investigations, pilot tests and reservoir simulations [10,16,32–34]. Additionally, polymer solutions require an optimized fluid chemistry in order to have the desired viscosity in the reservoir or rather a mobility ratio of the whole fluid system. Hereby, polymer EOR applications have to consider reservoir depth, reservoir temperature, reservoir thickness, porosity, permeability, oil gravity, oil viscosity and water chemistry (especially salinity and hardness) [35]. All these factors can decrease the quality of the injected polymer solutions which potentially results in an unfavorable polymer solution viscosity. In turn, this can result in economical as well as technical unfeasibility. These geological and fluid characteristics do not only influence the viscosity of the injected polymer solution, but also the viscoelasticity which is believed to contribute to the oil recovery as well. In situ rheology is the name given to the related aspects of rheology of polymeric solutions as they flow through porous media. EOR polymers, depending on the rate or time of deformation, can either store energy (an elastic response), dissipate energy (viscous response), or both. This is often termed as the shear-thinning and shear thickening behaviour in rheological terms. As previously mentioned, EOR viscoelastic polymers can also exhibit notorious resistance to stretching (high extensional viscosity) compared to the behaviour obtained when polymers are only under shear. EOR polymers, which have been utilised lately for flooding applications and which tend to be high molecular weight polymers (such as partially hydrolysed polyacrylamides (HPAM) along with biopolymers). Note that according to literature and the later shown data in this work, the viscoelastic property is most likely to be depicted Polymers 2020, 12, 2276 3 of 43 with high molecular weight polymers and seemly high concentrations. Due to this property, as well as solution concentrations, these polymer solutions may show a combination of viscous and elastic properties, known as viscoelasticity. This becomes of high importance since the fluid is forced to change its own speed to be able to maintain a fixed volumetric rate while crossing over the pores. As a result, extensional forces are generated in the flow path simultaneously with the fluid being under shear forces close to the wall areas. All these properties are best described and defined by different devices or rheometer that relate the connection between the stress (forces) and strain rate (deformation) tensors under different flow conditions. The constitutive equations that are often applied in the field of continuum mechanics are also useful. We present data that cover the areas of shear thinning, shear thickening and elastic turbulence, all associated to the interpretations of the possible existence of viscoelastic properties/behaviour. An additional element is the elastic turbulence, which differs from shear thickening. Reported results by Hincapie et al. [29], Rock et al. [30], Groisman and Steinberg [31] and other authors, point out that at low Reynolds numbers, elastic turbulence occurs. Polymers with high elasticity change the stability of the laminar flow causing elastic instabilities. This means the elastic turbulence is likely to occur at the pore level and represents a more recent interpretation on the effects in porous media. Overall, this shows the necessity of polymer solution optimization and especially, the requirement for a viscoelasticity-focused optimization approach. In order to account for the latter, it is imperative to understand the EOR polymers’ viscoelastic behavior in all its different shades.

1.2. Scope of the Study The present work aims to provide an extensive review of the importance of polymers’ viscoelasticity (if depicted) and their associated flow behavior in EOR applications. This helps to optimize the aqueous polymer solutions injected in oil reservoirs, develop and test new viscoelastic polymers, understand their degradation in the reservoir, their recovery mechanisms and finally, be able to assess the viscoelasticity’s importance in polymer flooding. This is achieved by reviewing and discussing the following aspects:

Effect of polymer viscoelasticity, different polymer chemistries, polymer molecular weight • distributions and concentrations on the oil recovery; Effect of reservoir properties on polymer viscoelasticity and its related recovery efficiency; • Effect of thermal, chemical, mechanical and chemical degradation on the polymer’s viscoelastic • flow behavior; Contribution and importance of the viscoelastic flow characteristics on EOR. • In a general sense, this work has the scope to manifest the importance and potential of viscoelasticity in polymer EOR applications and, hence, underline the need for further comprehensive investigations.

1.3. Paper Organization This work is arranged in seven sections. The first section provides a brief and general introduction in polymer flooding and the role of fluid viscoelasticity in it. The second section gives an overview about the different polymer types used in EOR as well as a discussion on their properties. Subsequently, the third section represents an extensive review on the role of viscoelasticity in EOR applications. Within this section, a definition of viscoelasticity and an overview of experimental approaches for its investigation are given. Furthermore, the third section provides a discussion on the physics and mechanics behind viscoelasticity and specifically on the viscoelastic flow phenomena observed in porous media. Moreover, the chemistry of viscoelastic polymers and the impacts on their flow behavior is reviewed. The following fourth section aims to critically discuss the viscoelastic recovery mechanisms and their importance on EOR. In the fifth section, the importance of viscoelasticity in polymer EOR applications, its potential, synergies and impacts are summarized. Following this, a summary and detailed conclusion of the study are given. Polymers 2020, 12, 2276 4 of 43

Polymers 2020, 12, 2276 4 of 43 2. Polymers for Enhanced Oil Recovery (EOR): Types and Chemistry 2. Polymers for Enhanced Oil Recovery (EOR): Types and Chemistry Although a wide range of polymers is available for EOR applications, there are basically two mainAlthough types of polymer: a wide range ﬁrst, syntheticof polymers polymers is available (e.g., polyacrylamides)for EOR applications, including there aare large basically variety two of modiﬁcationsmain types of inpolymer its chemistry;: first, synthetic and second, polymers biopolymers (e.g., polyacrylamides) which are mainly including polysaccharides a large variety that are of obtainedmodifications by biological in its chemistry processes; and at an second, industrial biopolymers scale. which are mainly polysaccharides that are obtained by biological processes at an industrial scale. 2.1. Synthetic Polymers 2.1. Synthetic Polymers Synthetic polymers are extensively used in EOR applications worldwide due to good understandingSynthetic polymersof the polymer are extensively system (e.g., used inter- in and EOR intramolecular applications interactionsworldwide dueand recoveryto good mechanisms),understanding their of the availability polymer and system relatively (e.g., inter low costs- and [36 intramolecular]. One of the simplest interactions and and most recovery widely usedmechanisms), synthetic their polymers availability used and in the relatively oil and low gas costs industry [36]. One are polyacrylamidesof the simplest and (PAMs) most [widely18,37]. Polyacrylamidesused synthetic polymers consist of used multiple in the acrylamide oil and gas monomers. industry are An poly acrylamideacrylamides molecule (PAMs is) [18,37].shown byPolyacrylamides Figure1a. It can consist be seen of multiple that an acrylamideacrylamide monomermonomers. consists An acrylamide of a hydrocarbon molecule chain is shown with by a double-boundFigure 1a. It can oxygen be seen atom that andan acrylamide an amino groupmonomer at one consists end ofof it.a hydrocarbon In order to generate chain with viscosifying a double- polyacrylamidesbound oxygen atom these and monomers an amino needs group to be at polymerized. one end of A it. common In order practice to generate for polymerization viscosifying ofpolyacrylamides acrylamide monomers these monomers is the use needs of ammoniumto be polymerized. persulfate A common as initiator practice and afor catalyst, polymerization namely tetramethylethylenediamineof acrylamide monomers is [38 the]. use The ofresulting ammonium PAM is persulfate shown in as Figure initiator1. and a catalyst, namely tetramethylethylenediamine [38]. The resulting PAM is shown in Figure 1. (a) (b)

H2C

O NH O NH 2 2

FigureFigure 1.1. ((aa)) AcrylamideAcrylamide monomermonomer usedused forfor polymerizationpolymerization ofof polyacrylamidespolyacrylamides (PAMs)(PAMs) (modified(modified afterafter LentzLentz etet al.al. [[39];39]; ((bb)) PAMPAM chainchain afterafter polymerizationpolymerization (modified (modified after after Hotta Hotta et et al. al. [ 40[40]]. . A linear PAM as shown in Figure1b has no significant gel strength which means that their A linear PAM as shown in Figure 1b has no significant gel strength which means that their viscosifying characteristics is degraded when experiencing mechanical stress such as shearing in the viscosifying characteristics is degraded when experiencing mechanical stress such as shearing in the porous reservoir rock [41]. Therefore, linear PAMs are additionally cross-linked in order to improve their porous reservoir rock [41]. Therefore, linear PAMs are additionally cross-linked in order to improve shear resistance which has a positive effect on the injectivity. For this purpose, methylenebisacrylamide their shear resistance which has a positive effect on the injectivity. For this purpose, is used in the polymerization process [38]. methylenebisacrylamide is used in the polymerization process [38]. The exemplary structure of a cross-linked PAM used in EOR applications is shown by Figure2. The exemplary structure of a cross-linked PAM used in EOR applications is shown by Figure 2. It can be seen that the red methylenebisacrylamide connects and cross-links the linear PAMs, thereby It can be seen that the red methylenebisacrylamide connects and cross-links the linear PAMs, thereby creating a three-dimensional complex structure. This complex structure enables the PAM to withstand creating a three-dimensional complex structure. This complex structure enables the PAM to higher mechanical stresses which is important during the flow through porous oil reservoirs, especially withstand higher mechanical stresses which is important during the flow through porous oil in cases where permeability is rather low. Other cross-linking agents commonly used are chromium reservoirs, especially in cases where permeability is rather low. Other cross-linking agents commonly (inorganic), phenol, formaldehyde, polyethylenimine and chitosan (all organic) [42]. Generally, used are chromium (inorganic), phenol, formaldehyde, polyethylenimine and chitosan (all organic) the decision as to which HPAM chemistry should be chosen is strongly dependent on different reservoir [42]. Generally, the decision as to which HPAM chemistry should be chosen is strongly dependent and fluid effects. Divers et al. [43] and Gaillard et al. [44] give detailed insights for definition and on different reservoir and fluid effects. Divers et al. [43] and Gaillard et al. [44] give detailed insights decision of the proper polymer type in different applications. Although PAMs are relatively good for definition and decision of the proper polymer type in different applications. Although PAMs are viscosifying agents, further modifications are made in order to increase its applicability in EOR. A very relatively good viscosifying agents, further modifications are made in order to increase its important characteristic of synthetic PAMs is their viscoelasticity which is explained in detail in applicability in EOR. A very important characteristic of synthetic PAMs is their viscoelasticity which Section3. In order to increase the viscoelasticity of a PAM, the amide groups of the PAMs can be is explained in detail in Section 3. In order to increase the viscoelasticity of a PAM, the amide groups hydrolyzed to a certain degree, forming a partially hydrolyzed polyacrylamide (HPAM). of the PAMs can be hydrolyzed to a certain degree, forming a partially hydrolyzed polyacrylamide (HPAM).

Polymers 2020, 12, 2276 5 of 43

Polymers 2020, 12, 2276 5 of 43 …

Polymers 2020, 12, 2276 … 5 of 43

CO CO

… …

NH NH CO CO CH CH2 2 NH NH NH NH NH2 NH2 CH CH2 2 CO CO CO CO NH NH NH2 NH2 … CH CH CH CH CH CH CH CH CH CH CH … CH2 2 2 2 2 2 CO CO n CO CO n CO CO … CH CH CH CH CH CH CH CH CH CH CH … CH2 2 2 2 2 2 n n NH NH2 CO CO n

CH2

NH NH2 n NH NH NH2 2 CH2 CO CO CO NH NH NH2 2 … CH CH CH CH … CH2 CH CH2 CH 2 2 CO CO n CO n CO … … CH CH CH CH CH2 CH CH2 CH 2 2 … n n

CO … Figure 2. Cross-linked PAM (red = methylenebisacrylamide, blue = PAM) (modified after National DiagnosticsFigure 2. Cross-linked [45]). PAM (red = methylenebisacrylamide, blue = PAM) (modified after National FigureDiagnostics 2. Cross [45-linked]). PAM (red = methylenebisacrylamide, blue = PAM) (modified after National Diagnostics [45]). An exemplary HPAM molecule structure is shown in Figure 3. HPAMs are widely used in oil- An exemplary HPAM molecule structure is shown in Figure3. HPAMs are widely used in recovery applications due to their excellent solubility characteristics in water and their strong oil-recoveryAn exemplary applications HPAM duemolecule to their structure excellent is solubilityshown in characteristics Figure 3. HPAMs in water are widely and their used strong in oil- thickening ability [46]. Nevertheless, the hydrolysis of PAMs transforms the polymer into a recoverythickening applications ability [46 due]. Nevertheless, to their excellent the hydrolysis solubility of characteristics PAMs transforms in water the polymer and their into strong a polyelectrolyte with negative charges which in turn react with cations of the reservoir brine [42]. This thickeningpolyelectrolyte ability with [46]. negative Nevertheless, charges which the hydrolysis in turn react of with PAMs cations transforms of the reservoir the polymer brine [into42]. a polyelectrolyteleadsThis to leads a high to a with highsensitivity negative sensitivity of chargesHPAMs of HPAMs which against against in solutionturn solution react water waterwith cationssalinity of andan thed is is reservoir one one of of the the brine major major [42]. issues issues This leadsregardingregarding to a highthe the HPAM HPAMsensitivity stability.stability. of HPAMs The The degree degree against of hydrolysisof solutionhydrolysis doeswater does not salinity onlynot influenceonly and influence is one the viscoelasticityof thethe viscoelasticitymajor andissues regardingandthe the overall overall the stability HPAM stability of stability. polymer of polymer solutions,The degreesolutions, but of also hydrolysisbut the also viscosity the does viscosity in not general. only in general. Kulickeinfluence Kulicke and the Hörl viscoelasticity and [47 ]Hörl have [47] andhaveshown the shown overall that that the stability viscositythe vis ofcosity increasespolymer increases betweensolutions, between a hydrolysisbut alsoa hydrolysis the of viscosity 30–70% of 30 andin– 70%general. decreases and Kulickedecreases accordingly and accordingly Hörl for [47] a haveforhydrolysis a shown hydrolysis that below the below 30% vis andcosity 30% above andincreases 70%. above Spildobetween 70%. and Spildo a Saehydrolysis [ and48] explain Sae of [48]30 the–70% explain hydrolysis-related and decreases the hydrolysis accordingly viscosity-related forviscosityincrease a hydrolysis increase with an belowincreasewith an 30% in increase repulsive and abovein forcesrepulsive 70%. yielding Spildoforces to polymer yielding and Sae conformation to [48] polymer explain conformation which the takes hydrolysis up which a higher-related take s volume and thereby increases the viscosity of the solution. viscosityup a higher increase volume with and an thereby increase increases in repulsive the viscosityforces yielding of the solution.to polymer conformation which takes up a higher volume and thereby increases the viscosity of the solution. ( H C HC ) ( H C HC ) 2 m 2 n ( H C HC ) ( H C HC ) 2 m 2 n C O C O C O C O - NH2 O - Figure 3. Molecule of a partially hydrolyzedNH2 polyacrylamideO (modified after Zhu et al. [46]). Figure 3. Molecule of a partially hydrolyzed polyacrylamide (modified after Zhu et al. [46]). Another chemical factor influencing not only viscoelasticity but also the viscosity of aqueous Figure 3. Molecule of a partially hydrolyzed polyacrylamide (modified after Zhu et al. [46]). polymerAnother solutions chemical is the factor charge influencing density. Spildonot only and viscoelasticity Sae [48] have but shown also thatthe forviscosity a HPAM of aqueous with polymerequalAnother molecular solutions chemical weightis the factor charge and hydrolysisinfluencing density. Spildo degree not only and but viscoelasticity diSaefferent [48] have charge shownbut densities, also that the for the vi ascosity viscosity HPAM of with as aqueous well equal as the viscoelasticity vary. Hereby, the polymer solution with a broad charge distribution has polymermolecular solutions weight isand the hydrolysis charge density. degree Spildo but different and Sae [48]charge have densities, shown that the for viscosity a HPAM as withwell equalas the shown a lower viscosity/viscoelasticity whereas the one with a narrower distribution had a higher molecularviscoelasticity weight vary. and Hereby, hydrolysis the degree polymer but solution different with charge a broad densities, charge the distribution viscosity as has well shown as the a viscosity/viscoelasticity in comparison. viscoelasticitylower viscosity/viscoelasticity vary. Hereby, the whereas polymer the solution one with with a a broad narrower charge distribution distribution had has shown a higher a Apart from charge density and hydrolysis, also the molecular weight has an influence on the lowerviscosity/viscoelasticity viscosity/viscoelasticity in comparison. whereas the one with a narrower distribution had a higher viscosity or rather viscoelasticity. This can be explained by the previous argument of Spildo and Sae [48] viscosity/viscoelasticityApart from charge in density comparison. and hydrolysis, also the molecular weight has an influence on the once again. In order to create a polymer molecule with a high molecular weight it is necessary to add viscosity or rather viscoelasticity. This can be explained by the previous argument of Spildo and Sae upApart single PAMfrom moleculescharge density to a long and chain hydrolysis, and if the length—therebyalso the molecular the numberweight ofhas PAMs—increases an influence on the the [48] once again. In order to create a polymer molecule with a high molecular weight it is necessary to viscositymolecular or rather weight viscoelasticity. increases due to This an increasingcan be explained volume occupation.by the previous Furthermore, argument a of longer Spildo polymer and Sae add up single PAM molecules to a long chain and if the length—thereby the number of PAMs— [48]chain once has again. more In hydrolyzed order to create backbones a polymer which molecule increase thewith fluid a high interactions. molecular weight it is necessary to addincreases up single the molecular PAM molecul weightes to increases a long chain due toand an ifincreasing the length volume—thereby occupation. the number Furthermore, of PAMs— a increaseslonger polymer the molecular chain has weight more hydrolyzedincreases due backbones to an increasing which increase volume the occupation. fluid interactions. Furthermore, a longer polymer chain has more hydrolyzed backbones which increase the fluid interactions.

Polymers 2020, 12, 2276 6 of 43

Overall, HPAM solutions have promising viscosifying and viscoelastic characteristics, but are also very sensitive to salt, mechanical stress and temperature. Therefore, hydrophobic association polymers (HAPAMs) were invented to overcome the disadvantages of HPAM solutions. HAPAMs are PAMs to which hydrophobic side-chains are connected. This not only decreased HPAMs/PAMs sensitivity against salinity and mechanical degradation, but also improved the polymer solution properties such as an enhanced viscosity, fluid–fluid interactions and also the ability to form emulsions. Although HAPAMs show encouraging results in laboratory measurements, it is important to mention that these polymers have not been studied in field applications yet and, therefore, there is a lack of understanding about them [49]. Another modification of PAMs is KYPAM which is an aromatic hydrocarbon monomer with an ethylene group. Thereby, KYPAM has a higher resistance against salt and because of the repulsion between its hydrophobic groups -resulting in stretched polymer chains- a higher viscosity compared to HPAMs [17]. In addition to a PAM and its different modifications, another synthetic polymer is 2-acrylamide-2-methyl propanesulphonate (AMPS) which is made up of anionic sulphonate protecting the acrylamide groups of its molecule and yielding to a good stability in high salinity brine. The acrylamide groups of AMPS lead to a good thermal stability as well as to a remarkable resistance against acidic and alkaline environments and hydrolysis [17].

2.2. Biopolymers Another type of polymer which is more often used in EOR application currently are biopolymers. These polymers are used because they are not officially listed as chemicals and, therefore, can be applied more easily, even in countries with very strict health, safety and environment regulations. Since this study aims to provide an extensive review on the viscoelasticity of polymers in EOR applications, biopolymers are not explained in detail here due to their missing viscoelastic properties. Nevertheless, a small paragraph is dedicated to this kind of polymer in order to complete the list of different polymer types. A major difference between synthetic and biopolymers is their origin. Whereas HPAMs are synthesized from monomers, biopolymers are typically obtained by fermentation in which bacteria produce the polymer as a result of their metabolic processes. The most widely used bacteria is Xanthomas campestris from which the biopolymer xanthan is derived. Another recently discussed biopolymer is schizophyllan which is also a polysaccharide [50]. The molecular weight of biopolymers is low in comparison to synthetic polymers which results in a relatively rigid molecule structure. As a result of this, biopolymers are excellent viscosifying agents which can be used in high-salinity water. Additionally, biopolymers show remarkable shear resistance due to their rigid structure. A disadvantage of these polymers is the high sensitivity to thermal degradation as well as the lack of polymer retention on the rock surface which means that there are no resistance effects after polymer flooding. Furthermore, biopolymers, due to their low molecular weight and missing hydrolyzed backbones, show no viscoelastic properties which can be understood as a significant disadvantage in EOR applications as the results from Hincapie et al. [29] and Needham and Doe [51] indicate.

3. Viscoelasticity in Enhanced Oil Recovery This section provides an extensive review on the viscoelastic flow phenomena encountered during the flow in porous media, e.g., in EOR applications. It gives a definition of viscoelasticity itself, the different experimental studies performed in literature and the mechanics during the viscoelastic fluid flow. Furthermore, the various impacts on the polymers’ viscoelasticity are discussed in detail in order to understand and outline the necessity of polymer solution optimization in enhanced oil recovery. Polymers 2020, 12, 2276 7 of 43

Polymers 2020, 12, 2276 7 of 43 The key aspects in optimising polymer rheology for EOR applications need to be examined in neglected.order to improve As previously process performance. described by Until Hincapie recently, [8] research and Hincapie investigating and the Ganzer complementarity [52], non-linear of different rheological techniques to fully characterise polymers used for EOR has been surprisingly viscoelastic experiments measured on a rotational rheometer can be used to provide an explanation neglected. As previously described by Hincapie [8] and Hincapie and Ganzer [52], non-linear for viscoelastic polymer behaviour related to porous media and to determine the influences of the viscoelastic experiments measured on a rotational rheometer can be used to provide an explanation environmental conditions. Different evaluations allow the possible determination of polymer for viscoelastic polymer behaviour related to porous media and to determine the influences of viscoelasticthe environmental properties conditions. from a rheological Different point evaluations of view. allow The themeasurements possible determination described include of polymer steady shearviscoelastic viscosity, properties small amplitude from a rheological oscillatory point shear of view.(SAOS, The stress measurements relaxation), described N1 (streamline include steady tension) and extensional thickening (strain hardening). This is to demonstrate the complementarity of shear viscosity, small amplitude oscillatory shear (SAOS, stress relaxation), N1 (streamline tension) differentand extensional rheological thickening techniques (strain to hardening). fully characterise This is to polyme demonstraters used the for complementarity EOR. Moreover, of di itff erentdepicts howrheological non-linear techniques viscoelastic to fully measurements characterise polymers performed used on for a EOR.rotational Moreover, rheometer it depicts can how be non-lineara useful tool to relateviscoelastic the behaviour measurements of viscoelastic performed polymers on a rotational to that in rheometer porous media. can be a useful tool to relate the behaviourEvaluations of viscoelastic are often polymersperformed to taking that in porousinto account media. the different effect of degradation, named thermalEvaluations and mechanical, are often often performed described taking in the into literature. account the different effect of degradation, named thermal and mechanical, often described in the literature. 3.1. Viscoelasticity as Per Definition 3.1. Viscoelasticity as Per Definition In order to understand the concept of viscoelasticity it helps to first define the standard equation In order to understand the concept of viscoelasticity it helps to first define the standard equation for an incompressible, isotropic Newtonian fluid in which the shear viscosity is related to shear stress for an incompressible, isotropic Newtonian fluid in which the shear viscosity is related to shear stress and rate by; and rate by; τ휏 η휂== (1) γ훾 (1) 1 wherewhere η isη isthe the shear shear viscosity viscosity in in Pa.s, ττ isis the the shear shear stress stress in in Pa Pa and andγ is γ the is the shear shear rate rate in s− in[ 53s−1]. [53 For]. aFor a NewtonianNewtonian fluid fluid this this relation relation is linear proportional.proportional. In In comparison comparison to to a a non-viscoelastic, non-viscoelastic, Newtonian Newtonian fluid,fluid, the the correlation correlation shown byby Equation Equation (1) (1) is non-linear is non-linear for a viscoelasticfor a viscoelastic fluid, e.g., fluid, anaqueous e.g., an HPAMaqueous HPAMsolution. solution. The non-linearity The non-linearity of shear viscosity, of shear shear viscosity, stress and shear rate stress are the and result rate of the are viscoelastic the result fluids’ of the ability to store (elastic behavior) and dissipate energy (viscous behavior) when the fluid molecule viscoelastic fluids’ ability to store (elastic behavior) and dissipate energy (viscous behavior) when the undergoes deformation, such as during the flow through narrow pore channels in reservoirs [30]. fluid molecule undergoes deformation, such as during the flow through narrow pore channels in Furthermore, if a completely viscous fluid is deformed stress immediately reduces to zero once the reservoirs [30]. Furthermore, if a completely viscous fluid is deformed stress immediately reduces to strain is constant [54]. For a completely elastic solid no relaxation would be observed. Figure4 zero once the strain is constant [54]. For a completely elastic solid no relaxation would be observed. illustrates the concept of the instantaneous relaxation of a Newtonian fluid and the time-dependent Figurerelaxation 4 illustrates of a fluid the which concept has elasticof the andinstantaneous viscous characteristics. relaxation of a Newtonian fluid and the time- dependent relaxation of a fluid which has elastic and viscous characteristics.

t0 t1 t2 t3 ELASTIC

t0 t1

VISCOELASTIC

VISCOUS Figure 4. Illustration of elastic, viscous and viscoelastic behavior. Figure 4. Illustration of elastic, viscous and viscoelastic behavior.

This relaxation behavior can also be translated into a relaxation modulus: 휏(푡) 퐺(푡) = (2) 훾 where G is the relaxation modulus in Pa [53]. Some researchers, e.g., Hincapie and Ganzer [52], Hincapie [8], Macosko [54] and Mezger [53] additionally distinguish between an elastic modulus G’ (energy storage) and viscous modulus G’’ (energy loss) exists. Based on these two moduli the

Polymers 2020, 12, 2276 8 of 43

This relaxation behavior can also be translated into a relaxation modulus:

τ(t) G(t) = (2) γ where G is the relaxation modulus in Pa [53]. Some researchers, e.g., Hincapie and Ganzer [52], Hincapie [8], Macosko [54] and Mezger [53] additionally distinguish between an elastic modulus G’ (energy storage) and viscous modulus G” (energy loss) exists. Based on these two moduli the relaxation time λ can be determined which is accepted to be a characteristic measure to quantify viscoelasticity [55–57]. The correlation between stress relaxation and strain given by Equation (2) is linear for γ < 0.5. This is also known as the plateau modulus Ge or linear-viscoelastic behavior. For γ > 1, the correlation is not linear anymore and therefore, in the deﬁnition of viscoelasticity it is necessary to distinguish between linear and non-linear viscoelasticity [54].

3.1.1. Linear Viscoelasticity Linear viscoelasticity can be mathematically described by the model proposed by Macosko [54] which is: Z t N X t t0 . λ− τ = Gk e− k γ(t0)dt0 (3) −∞ k=1 where t is the time in s and t’ the past time running from the inﬁnite past in s. A problem of the −∞ linear viscoelasticity model is the simpliﬁed assumption of an ideal shear situation, which means that the actual shear tensor has only two components. Therefore, the model given by Equation (3) does not represent a three-dimensional viscoelasticity and because of that it is not capable of predicting the stresses normal to the two-dimensional shear plane. This shows that for very low shear rates the shear viscosity does not depend on the shear rate. However, this model is only applicable at for γ < 0.5.

3.1.2. Non-Linear Viscoelasticity As discussed above, the model of linear viscoelasticity does not account for normal stresses and, hence, another model has to be introduced describing the so called non-linear viscoelasticity. This model accounts for γ > 1 with: τ(t, γ) G(γ, t) = (4) γ Thereby, the normal stresses and torsion which can occur during shearing or rather flow of a fluid. Stress response calculations for non-linear viscoelastic fluids can be made by using differential equations such as the Maxwell-type (Equation (4)), Kaye–Bernstein–Kearsley–Zapas-type (K-BKZ) (Equation (5)) or the Lodge equation (Equation (6)). Due to their long and complex form their derivation is not part of this study but are explained in detail in Macosko [54]. However, this researcher proposed to use the neo-Hookean (Equation (7)) model for stress response modelling in the most cases:

Maxwell type : τ + λ (τ) + f (τ, D) = 2µD (5) − ∇ Z t h 1i K BKZ type : τ = M φ B + φ B− dt0 (6) − − 1 2 −∞ Z t Lodge : τ = M [(t t0)B(t, t0)dt0 (7) − −∞ Neo Hookean : τ = GB (8) − dG(t) where M is a memory function of the ﬂuid depending on time M(t) = ), φ and φ are time − dt 1 2 derivates of the shear stress during relaxation at two consecutive time steps and B is a tensor describing the deformation of the ﬂuid at any point [54]. Polymers 2020, 12, 2276 9 of 43

3.1.3. Normal Stress Difference, N1 Another important quantity in the description of fluid viscoelasticity is the normal stress difference N1 and N2 whereas only N1 is discussed in this paragraph due N2’s measurement complexity and empirical origin. N1 is the quantification of fluid elasticity during the flow. As mentioned before, viscoelastic fluids experience a three-dimensional deformation during the flow and, therefore, the deformation of the fluid is represented by a 3 3 tensor containing three normal stresses σxx, σyy, × σzz and six shear stresses. It is important to note that in a viscous force-dominated flow only one shear stress is observed. Based on this 3 3 fluid deformation tensor it is possible to define the first normal × stress difference as; N = σxx σyy (9) 1 − whereas N1 is in Pa. Macosko [54] reports that the first normal stress difference is always positive for isotropic viscoelastic materials [58]. Hincapie [8] discussed the effect of N1 on the oil recovery in porous media. It is stated that N1 can be used as a parameter for the description of the elastic behavior of a polymer solution and that increasing oil recoveries can be observed for an increasing normal stress difference. Nevertheless, this observation has to be seen critically since it is not clear if the additional oil recovery is the result of an increased N1 or of other effects such as viscoelastic flow instabilities. It can be assumed that with increasing N1, the degree of elastic turbulence increases resulting in an incremental oil recovery.

3.1.4. Weissenberg Number In literature there are some dimensionless numbers used to describe the flow characteristics of viscoelastic properties. One of these numbers is the Weissenberg number Wi given by the following equation: . Wi = λγ (10) The number describes the non-isotropic arrangement of the polymer under shear stress and by that, gives a quantification of the elasticity and non-linearity of the fluid’s mechanical properties. For Wi = 0, the fluid behaves only viscous whereas for Wi > 0, the fluid shows elastic characteristics as well [59]. The Weissenberg number increases towards the injection and production wells due to a high 1 shear rate (up to 100 s− ) and decreases in the reservoir between the wells. It is important to mention that Wi is usually higher at the injection well rather than at the production well, because the polymer undergoes degradation in the reservoir and, hence, the polymer solution has a lower relaxation time than at the injection well.

3.1.5. Deborah Number Another important dimensionless number describing the fluid’s viscoelastic behavior is the Deborah number De which is defined by: v De = λ s (11) L where vs is the superficial flow velocity of the fluid in m/s and L the flow length along which the fluid flows in m. In addition to the previously defined Weissenberg number, the Deborah number allows for a quantification of the elastic strain [25,60]. In contradiction to the definition given by Howe et al. [25], Macosko [54] defines De as the ratio of relaxation time to the characteristic flow time t (De = λ/t). Moreover, Clarke et al. [55] defines the deformation of the polymer solution as viscoelastic for De > 1 and viscous for De < 1. The Deborah number value can vary throughout the reservoir and is not as easy to predict as Wi. First of all, the relaxation time of the polymer decreases from the injection well towards the production well due to polymer degradation. This would indicate that De decreases along the flow path in the reservoir. Furthermore, with increasing flow path length the Deborah number decreases as well. But since De is dependent on vs as well fluctuations of De have to be expected in the Polymers 2020, 12, 2276 10 of 43 reservoir. This can be due to varying permeability and porosities along the flow path which results in locally different superficial velocities.

3.1.6. M Parameter

Based on the previous definitions of Wi and De, another dimensionless parameter can be defined. The so called parameter M additionally acknowledge the elastic stress and stream curvature caused by viscoelasticity. M is defined by [61]: M = √Wi De (12)

3.2. Viscoelastic Flow Phenomena in Porous Media The state-of-the-art literature recognizes and discusses three different flow phenomena occurring in porous media. The phenomena are believed to be related to the viscoelastic nature of the polymer solutions, and can be classified as [8,62]:

(a) Shear thinning; (b) Shear thickening; and (c) Elastic turbulence.

This section discusses these viscoelastic ﬂow phenomena in detail.

3.2.1. Shear-Thinning Behavior As per rotational rheology definition, shear thinning is understood as a decreasing shear viscosity as a result of an increasing shear rate [54]. The behaviour can be seen from Figure5. Before the viscoelastic behavior of a polymer solution takes off, a small plateau with a stable viscosity trend can be observed, which is referred to as a Newtonian fluid behavior. Usually Newtonian behavior occurs at very low shear rates. After the flow has reached the first critical shear rate, the shear-thinning behavior starts. In these regions of shear rates, the flow is dominated by shear. According to Macosko [54] shear thinning of viscoelastic polymers solutions can be explained by the molecular entanglement of the polymer. The viscosity of polymer solutions is also a result of entanglement. In order to generate entanglement of polymer molecules, the chains have to be close enough to each other and they have to be present in a defined volume for a finite time. With increasing shear rate, the polymer molecules’ motion relative to each other increases and as a result the density of entanglement is reduced, hence decreasing the polymer solution’s viscosity causing shear thinning behavior. It is important to mention that the critical shear rates shown in Figure5 are only exemplary and can di ffer between different polymer types, solution properties as well as different porous media. The shear-thinning behavior was also experimentally investigated and extensively analyzed by Hincapie [8], Rock et al. [30], Tahir et al. [20,63] and Sheng [14] among many other researchers. Polymers 2020, 12, 2276 11 of 43 Polymers 2020, 12, 2276 11 of 43

FigureFigure 5.5. Viscoelastic ﬂowflow behaviorbehavior illustratedillustrated inin aa shearshear raterate vs.vs. apparentapparent/shear/shear viscosityviscosity plot.plot.

3.2.2. Shear-Thickening Behavior 3.2.2. Shear-Thickening Behavior ApartApart fromfrom thethe shear-thinning shear-thinning behavior, behavior, usually usually a shear-thickeninga shear-thickening behavior behavior can can be observedbe observed for polymersfor polymers injected injected in porous in porous media, media, such as such micromodels, as micromodels, sandstones sandstones or sand packs. or sand Shear packs. thickening Shear canthickening be generally can be defined generally as an defined increasing as viscosityan increasing due to viscosity an increasing due to shear an rateincreasing [64]. Shear-thickening shear rate [64]. behaviorShear-thickening can be observed behavior after can thebe polymerobservedflow after has the reached polymer the flow second has criticalreached shear the second rate as showncritical inshear Figure rate5 .as A shown remarkable in Figure observation 5. A remarkable that can observation be made from that thiscan be plot made is that from shear this thickeningplot is that isshear only thickening encountered is only in porousencountered media in duringporous media polymer during flooding polymer and flooding not in rotational and not in rheometer rotational measurementsrheometer measurements [8,20,26,27,63 [8,20,26,27,63,65,65–68]. It is believed–68]. It thatis believed the missing that shearthe missing thickening shear is thickening the result ofis thethe missingresult of flow the motion, missing since flow the motion, viscosity since increase the is viscosity commonly increase explained is withcommonly a distinctive explained stretching with of a thedistinctive polymer stretching molecule [of27 the,69]. polymer Because molecule of this stretching [27,69]. andBecause the highof this shear stretching rate, the and polymer the high molecule shear hasrate, no the su ffi polymercient time molecule to re-coil has itself. no By sufficient that, the polymer time to flowre-coil is dominated itself. By that by elongational, the polymer forces flow and is thedominated viscosity by increase elongational is referred forces to and as elongational the viscosity viscosity increase oris referred extensional to as viscosity elongational [14,58 viscosity,62,70–72 or]. extensionalAnother viscosity explanation [14,58,62,70 for shear–72] thickening. is given by Hincapie et al. [29]. The authors investigated the polymerAnother flow explanation in porous for media shear quantitatively thickening and is given qualitatively. by Hincapie By combining et al. [29]. both The input authors data, itinv wasestigated possible the to polymer relate the flow additional in porous viscosity media or quantitatively rather the additional and qualitatively. pressure drop By along combining the porous both mediainput data, to viscoelastic it was possible flow instabilities. to relate theThe additional streamline viscosity instabilities or rather cause the theadditional polymer pressure molecules drop to flowalong on the a longer porous path media through to viscoelastic the porous flow media instabilities. and thereby The generating streamline an additionalinstabilities di causefferential the pressure.polymer molecules So, as a consequence to flow on ofa longer the work path of Hincapiethrough the et al.porous [29], shearmedia thickening and thereby is actually generating not anan increaseadditional in fluid differential viscosity, pressure. but only So, an as additional a consequence pressure. of Similar the work observations of Hincapie have et beenal. [29], made shear by Clarkethickening et al. is [55 actually], Tahir et no al.t an [20 increase,63] and Galindo-Rosalesin fluid viscosity, et but al. [61 only]. an additional pressure. Similar observations have been made by Clarke et al. [55], Tahir et al. [20,63] and Galindo-Rosales et al. [61]. 3.2.3. Elastic Turbulence

3.2.3.The Elastic most Turbulence widely and recently discussed viscoelastic flow phenomena occurring in porous media is the so called elastic turbulence. Elastic turbulence can be defined as flow instabilities occurring The most widely and recently discussed viscoelastic flow phenomena occurring in porous media due to the viscoelasticity of the injected polymer solutions. The first to describe the viscoelastic flow is the so called elastic turbulence. Elastic turbulence can be defined as flow instabilities occurring due instabilities during the flow of aqueous polymer solutions were Groisman and Steinberg [31]. In their to the viscoelasticity of the injected polymer solutions. The first to describe the viscoelastic flow model, a step increase in the elastic stress is assumed to be the reason for the onset of elastic turbulence. instabilities during the flow of aqueous polymer solutions were Groisman and Steinberg [31]. In their The density of elastic stress of a viscoelastic flow can be estimated with W ν/2 (ν is the elastic stress) model, a step increase in the elastic stress is assumed to be the reasoni for the onset of elastic and was observed to be up to 65 times larger in the turbulent flow regime compared to the laminar flow. turbulence. The density of elastic stress of a viscoelastic flow can be estimated with Wi ν/2 (ν is the elastic stress) and was observed to be up to 65 times larger in the turbulent flow regime compared to the laminar flow.

Polymers 2020, 12, 2276 12 of 43

Polymers 2020, 12, 2276 12 of 43 Furthermore, Groisman and Steinberg [31] describe the evolution of the viscoelastic flow Furthermore, Groisman and Steinberg [31] describe the evolution of the viscoelastic flow instabilities. Firstly, and because of the extensive polymer molecule stretching, an unstable and instabilities. Firstly, and because of the extensive polymer molecule stretching, an unstable and irregular secondary flow is introduced. This secondary flow further influences the polymer molecules irregular secondary flow is introduced. This secondary flow further influences the polymer molecules resulting in a further stretch which creates an even more distinctive flow instability until a complete resulting in a further stretch which creates an even more distinctive flow instability until a complete irregular, dynamic flow is established in the porous media. Based on the work from Groisman irregular, dynamic flow is established in the porous media. Based on the work from Groisman and and Steinberg [31] which mainly analyzed the elastic turbulence on a quantitative basis, other Steinberg [31] which mainly analyzed the elastic turbulence on a quantitative basis, other researchers researchers performed experimental investigations with a more qualitative focus describing the performed experimental investigations with a more qualitative focus describing the instabilities’ instabilities’ characteristics. characteristics. Howe et al. [25], for example, investigated viscoelastic flow instabilities as well. They present Howe et al. [25], for example, investigated viscoelastic flow instabilities as well. They present streamline photographs made during their flow experiment in micromodels that show the elastic streamline photographs made during their flow experiment in micromodels that show the elastic turbulence phenomenon. Furthermore, they show a correlation between the elastic turbulence and the turbulence phenomenon. Furthermore, they show a correlation between the elastic turbulence and onset of shear thickening of viscoelastic polymer solutions. Clarke et al. [55] also presented streamline the onset of shear thickening of viscoelastic polymer solutions. Clarke et al. [55] also presented images of elastic turbulent flow in micromodels. However, these images show a lack of quality not streamline images of elastic turbulent flow in micromodels. However, these images show a lack of enabling a detailed description of the viscoelastic flow instabilities’ characteristics. quality not enabling a detailed description of the viscoelastic flow instabilities’ characteristics. Galindo-Rosales et al. [61] also performed experimental micromodel studies in order to investigate Galindo-Rosales et al. [61] also performed experimental micromodel studies in order to the elastic turbulent behavior of viscoelastic polymer solutions. For that, these researchers injected investigate the elastic turbulent behavior of viscoelastic polymer solutions. For that, these researchers PAA solutions at various concentrations and flow rates into symmetric micromodels. Although they injected PAA solutions at various concentrations and flow rates into symmetric micromodels. were able to observe flow instabilities by streamline visualization, it was not possible to describe the Although they were able to observe flow instabilities by streamline visualization, it was not possible qualitative characteristics of the flow due to image-quality issues. to describe the qualitative characteristics of the flow due to image-quality issues. A common problem of these studies is the utilization of symmetric micromodels which are A common problem of these studies is the utilization of symmetric micromodels which are not not resembling the complex porous structure of reservoir rocks as encountered in EOR applications. resembling the complex porous structure of reservoir rocks as encountered in EOR applications. An An overview of the recent evolution of streamline imaging during elastic turbulent flow is shown by overview of the recent evolution of streamline imaging during elastic turbulent flow is shown by Figure6. From this figure it can be clearly seen that all researchers, apart from Hincapie et al. [ 29], Figure 6. From this figure it can be clearly seen that all researchers, apart from Hincapie et al. [29], use simplified porous structures which do not represent the complexity of real reservoir rocks. use simplified porous structures which do not represent the complexity of real reservoir rocks.

- Detailed description of elastic turbulence characterisitcs in porous media resembling real reservoir rock.

- Comprehensive micromodel study combining streamline imaging and a range of quantitative measurements allowing to determine correlations between flow patterns and fluid properties

- Advanced micromodel study of elastic turbulence using methods such as average velocity mapping

- Streamline imaging of different flow patterns in symmetric channel micromodels

- Description of elasticity effects on the flow in hyperbolic structures at various flow rates.

- First ones to describe elastic turbulence of polymer solutions

Figure 6. Recent evolution of elastic turbulence visualization (based on Groisman and Steinberg [31], SousaFigure et 6. al.Recent [73], Galindo-Rosalesevolution of elastic et al.turbulence [61], Scholz visualization et al. [59], Howe(based eton al. Groisman [25], Hincapie and Steinberg et al. [29]). [31], Sousa et al. [73], Galindo-Rosales et al. [61], Scholz et al. [59], Howe et al. [25], Hincapie et al. [29]).

Polymers 2020, 12, 2276 13 of 43

The work performed by Hincapie et al. [29] accounts for this problem by using glass-silicon-glass (GSG) micromodels generated based on Bentheimer sandstone micro CT images. By this and using state-of-the-art imaging equipment and methods it was possible to describe the elastic turbulence phenomenon of viscoelastic polymer quantitatively and qualitatively in a comprehensive manner. Figure7 shows the viscoelastic flow instabilities for a 1000 ppm aqueous polymer solution. The images show the streamline visualization for 10 and 100 µL/min in a GSG micromodel. The left and right image in each line have been taken in consecutive time steps of approximately 100 ms. As can be seen, for a flow rate of 10 µL/min there are actually no turbulence characteristics except from a changing flow width of the main stream (indicated by the red arrows) in the pore. Note that this behaviour was only observed for the HPAM solutions here included. In unpublished data from the authors, we have attempted to evaluate polysaccharide solutions (xanthan and others) without similar observations or Polymersconditions 2020,previously 12, 2276 listed. 14 of 43

10 µl/min 10 µl/min

100 µl/min 100 µl/min

Figure 7. Streamline visualization for a viscoelastic 1000 ppm polymer solution in a glass-silicon-glass Figure 7. Streamline visualization for a viscoelastic 1000 ppm polymer solution in a glass-silicon-glass (GSG) micromodel (modified after Hincapie et al. [29]). (GSG) micromodel (modified after Hincapie et al. [29]). Hincapie et al. [29] as well as Rock et al. [30] considered this flow behavior as a transitional flow regime. For 100 µL/min, these researchers observed various elastic turbulent flow characteristics. A remarkable observation is the streamline crossing (indicated by orange circles in Figure7) which can be described as an overlapping flow of two or more flow levels. The streamline crossing can be observed in particular near grain walls (black) and corners. Another observation from the streamline visualization is the build-up of vortices (indicated by pink circle). By comparison of the left with the right image in the second line, it can be observed that the vortex builds up and disappears within a few tens of ms, clearly illustrating the significant viscoelastic flow instabilities during the flow of the aqueous polymer solution. Another elastic turbulence characteristic that can be defined from Figure7 is the penetration of the stream into small corners as shown by the light blue rectangle. Again, this penetration is not permanent, but changes every few ms in an irregular manner. A last characteristic that can be observed from the flow visualization is the constantly changing direction of the main stream, which is illustrated by the light green arrows in the bottom images.

Figure 8. Apparent viscosity vs. shear rate measured in a GSG micromodel. The black lines illustrate the onset of the transitional flow pattern whereas the blue lines illustrate the onset of elastic turbulence (Rock [69]).

3.3. Experimental Approaches for the Assessment of Polymer Viscoelasticity This section provides an overview of experimental investigation methods used to determine the viscoelasticity of polymer solutions. Since many different studies on polymer viscoelasticity have been published over the last two decades, a broad range of experimental approaches, including quantitative and qualitative methods, is available. For the investigation of polymer viscoelasticity with regards to EOR applications, both, the fluid properties itself as well as the flow characteristics

Polymers 2020, 12, 2276 14 of 43

10 µl/min 10 µl/min

100 µl/min 100 µl/min

Polymers 2020, 12, 2276 14 of 43

As a summary of the streamline visualization, Hincapie et al. [29] defined the elastic turbulence characteristics as follows: (1) changing stream width, (2) changing stream direction, (3) penetration of the stream into small corners, (4) build-up and immediate collapse of vortices and (5) streamline crossing, especially near100 grains. µl/min Rock et al. [11] consider100 theµl/min penetration of small corners and build-up of vortices, in particular, as the main reason for an increased oil recovery due to viscoelastic effects, as observed by Clarke et al. [55]. This will be discussed in detail in the coming section. In addition to the qualitative analysis of Hincapie et al. [29], Rock [69] conducted in situ micromodel viscosity measurements. An exemplary measurement is shown by Figure8 which also includes the observed onset of elastic turbulence. As can be seen, the onset of shear thickening correlates with the onset of transitional flow. This underlines the previous assumption in Section 3.2.2 that shear thickeningFigure 7. is Streamline not an increasing visualization viscosity, for a viscoelastic but an additional 1000 ppm polymer pressure solution drop in along a glass the-silicon porous-glass media resulting(GSG in) micromodel a delusory (modified increased after viscosity. Hincapie Howe et al. et [29]). al. [25] and Galindo-Rosales et al. [61] have made similar correlations.

Figure 8. Apparent viscosity vs. shear rate measured in a GSG micromodel. The black lines illustrate Figure 8. Apparent viscosity vs. shear rate measured in a GSG micromodel. The black lines illustrate the onset of the transitional flow pattern whereas the blue lines illustrate the onset of elastic turbulence (Rockthe onset [69 ]).of the transitional flow pattern whereas the blue lines illustrate the onset of elastic turbulence (Rock [69]). 3.3. Experimental Approaches for the Assessment of Polymer Viscoelasticity 3.3. Experimental Approaches for the Assessment of Polymer Viscoelasticity This section provides an overview of experimental investigation methods used to determine the viscoelasticityThis sectio ofn polymerprovides solutions. an overview Since of manyexperimental different investigation studies on polymer methods viscoelasticity used to determine have been the publishedviscoelasticity over of the polymer last two solutions. decades, a Since broad many range ofdifferent experimental studies approaches, on polymer including viscoelasticity quantitative have beenand qualitative published methods, over the is last available. two decades, For the a investigation broad range of of polymer experimental viscoelasticity approaches, with regards including to quantitativeEOR applications, and qualitative both, the fluidmethods, properties is available. itself as For well the as theinvestigation flow characteristics of polymer in viscoelasticity porous media withneed regards to be investigated. to EOR applications, Therefore, both, this section the fluid is subdivided properties intoitself fluid as well property as the andflow flow characteristics effect parts.

3.3.1. Quantitative Fluid Property Evaluations

Fluid property evaluation usually considers a variety of rheological measurements including viscosity measurements, optical methods and in general chemical and physical properties. Here, only a focus on the viscoelasticity measuring methods is given, since this study focuses on the role of viscoelasticity in enhanced oil recovery applications.

Measurement of Relaxation Time As already mentioned, the relaxation time λ is one of the most important properties of a polymer solution describing its degree of viscoelasticity. Sousa et al. [73] describe diﬀerent devices that are capable of measuring the elongational relaxation time of viscoelastic polymer solutions. A suitable Polymers 2020, 12, 2276 15 of 43

in porous media need to be investigated. Therefore, this section is subdivided into fluid property and flow effect parts.

3.3.1. Quantitative Fluid Property Evaluations Fluid property evaluation usually considers a variety of rheological measurements including viscosity measurements, optical methods and in general chemical and physical properties. Here, only a focus on the viscoelasticity measuring methods is given, since this study focuses on the role of viscoelasticity in enhanced oil recovery applications.

Measurement of Relaxation Time Polymers 2020, 12, 2276 15 of 43 As already mentioned, the relaxation time λ is one of the most important properties of a polymer solution describing its degree of viscoelasticity. Sousa et al. [73] describe different devices that are rheometercapable of formeasuring relaxation the timeelongational measurements relaxation is, fortime example, of viscoelastic the filament polymer stretching solutions. extensional A suitable rheometerrheometer (FiSER) for relaxation [74–77]. time This rheometer measurements separated is, for the example end plates, the at filament an exponential stretching rate resulting extensional in arheometer constant deformation (FiSER) [74– rate.77]. This Another rheometer common separated device for the relaxation end plates time at measurementsan exponential is rate the capillaryresulting break-upin a constant extensional deformation rheometer rate. (CaBER Another™ common)[27,78,79 device]. A schematic for relaxation sketch time of the measurements measurement is with the acapillary CaBER™ breakcan be-up seen extensional in Figure9 . rheometer In a first stage (CaBER™) the polymer [27,78,79]. solution A is schematic introduced sketch between of two the cylindricalmeasurement plates, with usually a CaBER™ having can a diameter be seen between in Figure 4–6 9. mm. In a Asfirst a stageresult, the a fluid polymer bridge solution between is theintroduced two plates between of the two rheometer cylindrical is formed plates, (see usually step having 1 in Figure a diameter9). Subsequently, between 4– the6 mm. upper As platea result, is rapidlya fluid moved bridge upwards between and the consequently two plates aof fluid the filament rheometer is created is formed and the(see diameter step 1 in in the Figure middle 9). isSubsequently, measured over the time upper (see plate step is 2rapidly in Figure moved9). The upwards diameter and measurement consequently isa fluid taken filament by using is acreated light sourceand the and diameter camera [ in80 ]. the middle is measured over time (see step 2 in Figure 9). The diameter measurement is taken by using a light source and camera [80].

dmid(t)

Polymer

dplate

1 2

FigureFigure 9.9. MeasurementMeasurement processprocess ofof aa CaBERCaBER™™ rheometer.rheometer. ((11)) IntroducingIntroducing thethe polymerpolymer betweenbetween platesplates toto formform aa ﬂuidfluid bridge,bridge, ((22)) Rapid Rapid movement movement of of the the upper upper plate plate to to create create ﬁlament. filament.

OtherOther approachesapproaches ofof measuringmeasuring thethe relaxationrelaxation timetime ofof viscoelasticviscoelastic polymerpolymer solutionssolutions presentedpresented byby Sousa Sousa et et al. al. [ [73]73] areare thethe use use of of aa Rayleigh–OhnesorgeRayleigh–Ohnesorge jetjet elongationalelongational rheometerrheometer (ROJER) (ROJER) or or optically-detectedoptically-detected elastocapillary elastocapillary self-thinning self-thinning dripping-onto-subtract dripping-onto-subtract (ODES-DOS).(ODES-DOS). In particular, particular, thethe ROJERROJER rheometerrheometer isis capablecapable ofof measuringmeasuring relaxationrelaxation timestimes downdown toto 8080µ µs.s. InIn thethe workwork presentedpresented byby RockRock [[69],69], therethere havehave beenbeen problemsproblems withwith measuringmeasuring thethe relaxationrelaxation timestimes ofof somesome 500500 ppmppm HPAMHPAM solutions,solutions, becausebecause thethe KinexusKinexus rotationalrotational rheometerrheometer (Malvern(Malvern Instruments)Instruments) usedused inin thisthis researchresearch waswas notnot ableable toto measuremeasure thethe relaxationrelaxation times.times. Therefore,Therefore, aa quantitativequantitative characterizationcharacterization ofof thesethese solutionssolutions waswas limited.limited. Here,Here, the the ROJER ROJER rheometer rheometer can can solve solve these these problems problems and and hence, hence, should should be consideredbe considered for futurefor future relaxation relaxation time time measurements. measurement Rocks. Rock [69] measured [69] measured the elastic the elastic (energy (energy storage) storage) modulus modulus G’ and viscousG’ and (energy viscous loss) (energy modulus loss) G” modulus for various, G’’ increasing for various, shear increasing rates. Based shear on rates. this measurement Based on this it wasmeasurement possible to it determine was possible the to relaxation determine time the of relaxation the viscoelastic time of solution the viscoelastic by using, solution by using, 11 λ휆 = . ((13)13) γ훾overlaṗ표푣푒푟푙푎푝 where γoverlap is the shear rate at which the curve of G’ and G” overlap in the plot. However, and as mentioned before, this measuring method is only suitable for polymer solutions with relatively high viscoelasticity and consequently, a high relaxation time. Recently, Del Giudice et al. [81] presented a microfluidic approach to measure the shear relaxation time of viscoelastic fluids. The measurement principle is based on the flow behavior of solid particles in solution. For a stationary, laminar flow behavior of a Newtonian fluid the particles added to the fluid will move perpendicular to the flow direction in a microfluidic channel. Without inertia and in the constant-viscosity regime of aqueous viscoelastic polymer solutions, the added particles will move to the center line. By this difference in particle flow behavior it is possible to determine the shear relaxation time of diluted polymer solutions. Polymers 2020, 12, 2276 16 of 43 where γoverlap is the shear rate at which the curve of G’ and G’’ overlap in the plot. However, and as mentioned before, this measuring method is only suitable for polymer solutions with relatively high viscoelasticity and consequently, a high relaxation time. Recently, Del Giudice et al. [81] presented a microfluidic approach to measure the shear relaxation time of viscoelastic fluids. The measurement principle is based on the flow behavior of solid particles in solution. For a stationary, laminar flow behavior of a Newtonian fluid the particles added to the fluid will move perpendicular to the flow direction in a microfluidic channel. Without inertia and in the constant-viscosity regime of aqueous viscoelastic polymer solutions, the added Polymers 2020, 12, 2276 16 of 43 particles will move to the center line. By this difference in particle flow behavior it is possible to determine the shear relaxation time of diluted polymer solutions. A sketch ofof aa microfluidicmicrofluidic setup setup based based on on the the work work of of Del Del Giudice Giudice et et al. al. [81 [81]] is shownis shown in Figurein Figure 10. As10. itAs can it can be seen,be seen, the the viscoelastic viscoelastic polymer polymer solution solution with with solid solid particles particles added added to to it isit is injected injected over over a syringea syringe and and capillary capillary into into a microfluidica microfluidic channel channel which which has has a centerline. a centerline. In theIn the work work presented presented by Del by GiudiceDel Giudice et al. et [81 al.], [81], the micro the micro channel channel has a diameterhas a diameter of 100 ofµm 100 and µm a length and a oflength 7 cm. of Using 7 cm. the Us concepting the ofconcept particle of movementparticle movement discussed discussed before and before with and the with help ofthe a help microscope, of a microscope, it is possible it is topossible see whether to see thewhether injected the solutioninjected issolution viscoelastic. is viscoelastic.

Injection Syringe with Polymer-Particle-Solution Micro Channel

Non-Viscoelastic Fluid Viscoelastic Fluid Figure 10. 10.Microfluidic Microfluidic setup setup for measuringfor measuring relaxation relaxation time of time viscoelastic of viscoelastic polymer solutionspolymer (modified solutions after(modified Del Giudice after Del et Giudice al. [81]). et al. [81]). Moreover, by using empirical equations it is possible to calculate the shear relaxation time of the Moreover, by using empirical equations it is possible to calculate the shear relaxation time of the injected polymer solution. First of all, Romeo et al. [82] defined a dimensionless parameter θ which injected polymer solution. First of all, Romeo et al. [82] defined a dimensionless parameter θ which correlates De, the length Lmicro and Hmicro of the micro channel as well as the ratio β (= Dp/Hmicro correlates De, the length Lmicro and Hmicro of the micro channel as well as the ratio β (= Dp/Hmicro whereas Dp is the diameter of the added particles). The dimensionless parameter θ is given by: whereas Dp is the diameter of the added particles). The dimensionless parameter θ is given by:

Lmicro 2 1 4Q θ = De 퐿푚푖푐푟표 β = 1 π λ 4푄 (14) 2 3 휃 = 퐷푒 Hmicro 훽 = 2 휋 휆π D 3 (14) 퐻푚푖푐푟표 2 휋퐷 where Q is the injection rate and D is the diameter of the channel, since it is cylindrical shaped. where Q is the injection rate and D is the diameter of the channel, since it is cylindrical shaped. As As defined previously in Equation (10), a parameter k = 1 π is introduced to the definition of De in defined previously in Equation (10), a parameter k = ½ π is2 introduced to the definition of De in order order to transform the calculated relaxation time from s/rad to s. Furthermore, vs/L was changed to the to transform the calculated relaxation time from s/rad to s. Furthermore, vs/L was changed to the injection rate with the flow rate Q. injection rate with the flow rate Q. In order to be able to calculate the relaxation time, another equation is required, which is also In order to be able to calculate the relaxation time, another equation is required, which is also defined by Romeo et al. [82] and which is: defined by Romeo et al. [82] and which is: 1 f1 = 1 (15) C θ2 푓1 = 1 + B e 2 (15) 1 + 퐵 푒−−퐶 휃 where f 1 is the fraction of particles in the stream on the center line of the microfluidic channel, B and C where f1 is the fraction of particles in the stream on the center line of the microfluidic channel, B and are constants with best fits for B = 2.7 and C = 2.75. Substituting θ in Equation (13) with Equation (14) C are constants with best fits for B = 2.7 and C = 2.75. Substituting θ in Equation (13) with Equation leads then to the following final relaxation time equation: (14) leads then to the following final relaxation time equation: s 4 ! π 1 D 1 f1B λ = 2π 4 ln (16) 휋 12 퐷 1 푓1퐵 휆 = 2휋 4 β LQ √C ln(1 f1 ) (16) 2 − 4 훽 퐿푄 퐶 1 − 푓1 By changing the diameter of the micro channel, it is possible to measure even small values of relaxation time. Potential disadvantages are the empirical origin of the equations, especially for the constants C and B, the qualitative measurement (based on microscopy) and the missing confidence in the results, although Del Giudice et al. [81] showed a good correlation between measurements with the microfluidic approach and conventional rheometer.

Measurement of Shear Viscosity Although shear viscosity is not a property directly related to the viscoelasticity of aqueous polymer solutions, the shear thinning and thickening regime, and especially its onset, are inﬂuenced Polymers 2020, 12, 2276 17 of 43

By changing the diameter of the micro channel, it is possible to measure even small values of relaxation time. Potential disadvantages are the empirical origin of the equations, especially for the constants C and B, the qualitative measurement (based on microscopy) and the missing confidence in the results, although Del Giudice et al. [81] showed a good correlation between measurements with the microfluidic approach and conventional rheometer.

Measurement of Shear Viscosity PolymersAlthough2020, 12, 2276 shear viscosity is not a property directly related to the viscoelasticity of aqueous17 of 43 polymer solutions, the shear thinning and thickening regime, and especially its onset, are influenced byby the the viscoelasticity. viscoelasticity. Therefore,Therefore, this part of the section section focuses focuses onon the the viscosity viscosity measurement measurement of of viscoelasticviscoelastic polymers.polymers. AA simplesimple wayway ofof measuringmeasuring thethe viscosityviscosity ofof fluidsfluids isis thethe useuse ofof aa rheometerrheometer suchsuch asas aa rotationalrotational rheometerrheometer as as used used by by Hincapie Hincapie [ [8].8]. The results obtained from rheometerrheometer are are very very accurate accurate and and reproducible,reproducible, but but dodo not not represent represent the the rheologyrheology of of fluids fluids within within porousporous media. media. This This was was seenseen in in didifferentfferent works,works, e.g.,e.g., [[8,63,67,83]8,63,67,83] andand RockRock [[69].69]. Therefore,Therefore, itit isis necessarynecessary toto measuremeasure thethe rheologicalrheological propertiesproperties ofof the the viscoelastic viscoelasti polymerc polymer solutions solutions within within porous porous media. media. Moreover, Moreover, a combination a combination of both of rheometerboth rheometer data anddata data and obtaineddata obtained from floodingfrom flooding experiments experiments within within porous porous media media (e.g., sand(e.g., pack,sand corepack, plugs core andplugs micromodels) and micromodels) allows theallows correction the correction of the shear of the rate shear [60,63 rate,66, 72[60,63,66,72,84].,84]. This is necessary This is becausenecessary shear because rates shear are only rates calculated are only calculated in flooding in experiments flooding experiments and, hence, and have, hence, a certain have degree a certain of inaccuracy.degree of inaccuracy. The combination The combination of both data of sets both and data shear sets rate and correction shear rate can correction be seen in can Figure be 11seen. in Figure 11.

Figure 11. Example for shear rate correction (CF = correction factor) [69]. Figure 11. Example for shear rate correction (CF = correction factor) [69]. Another problem of rotational rheometer measurements regarding the evaluation of viscoelastic Another problem of rotational rheometer measurements regarding the evaluation of viscoelastic fluid properties and flow phenomena is the missing shear thickening of the polymers as obtained fluid properties and flow phenomena is the missing shear thickening of the polymers as obtained in in experiments in porous media. This can be seen in Figure 11 as well. This further underlines the experiments in porous media. This can be seen in Figure 11 as well. This further underlines the necessity of experiments in porous media in order to capture the full polymer rheology and, hence, necessity of experiments in porous media in order to capture the full polymer rheology and, hence, the shear viscosity measurement in porous media is explained below. the shear viscosity measurement in porous media is explained below. Although core flooding represents the most realistic approach of in situ polymer rheology Although core flooding represents the most realistic approach of in situ polymer rheology evaluation, micromodel flooding is here considered to be the best experimental approach due to its evaluation, micromodel flooding is here considered to be the best experimental approach due to its setup simplicity, fast measurement and reproducibility of results. Many different microfluidic setups setup simplicity, fast measurement and reproducibility of results. Many different microfluidic setups and approaches have been presented or rather proposed such as those from Galindo-Rosales et al. [61], and approaches have been presented or rather proposed such as those from Galindo-Rosales et al. Scholz et al. [59], Howe et al. [25], Clarke et al. [55], Campo-Deano et al. [85], Herbas et al. [86], Wegner [61], Scholz et al. [59], Howe et al. [25], Clarke et al. [55], Campo-Deano et al. [85], Herbas et al. [86], et al. [15], Sousa et al. [87], Hincapie [8] and Rock et al. [30]. Wegner et al. [15], Sousa et al. [87], Hincapie [8] and Rock et al. [30]. In the following, the experimental setup and workflow used for preliminary studies of this In the following, the experimental setup and workflow used for preliminary studies of this work work is presented and discussed. The setup presented in Figure 12 consists of a high-precision is presented and discussed. The setup presented in Figure 12 consists of a high-precision syringe syringe pump connected to an effluent collector and a differential pressure sensor (quantitative pump connected to an effluent collector and a differential pressure sensor (quantitative evaluation) evaluation) and the micromodel by PTFE tubes. All thread connections are additionally isolated by and the micromodel by PTFE tubes. All thread connections are additionally isolated by Teflon tape. Teflon tape. Furthermore, the micromodel is placed under a microscope equipped with a high-speed Furthermore, the micromodel is placed under a microscope equipped with a high-speed camera camera (qualitative evaluation). There is a broad range of micromodel types that can be used for

ﬂooding experiments such as GSG micromodels based on Bentheimer CT images [15,88,89], completely transparent real porous-media-resembling plastic micromodels (Hogeweg et al. 2018) and symmetric micromodels as presented in the work of Galindo-Rosales [61] and Scholz et al. [59]. An overview image of a GSG micromodel as used by Wegner et al. [15], Rock et al. [30], Gaol et al. [89,90] and Hincapie et al. [29] as an example is shown by Figure 13. In addition, valves are installed to allow evacuation of certain parts of the setup, e.g., removing gas bubbles in the pipes. Moreover, the syringe pump, diﬀerential pressure sensor, microscope and camera are connected to a computer enabling Polymers 2020, 12, 2276 18 of 43

(qualitative evaluation). There is a broad range of micromodel types that can be used for flooding Polymers 2020, 12, 2276 18 of 43 experiments such as GSG micromodels based on Bentheimer CT images [15,88,89], completely transparent(qualitative real evaluation). porous-media There-resembling is a broad plasticrange of micromodels micromodel (Hogewegtypes that canet al. be 2018) used and for floodingsymmetric micromodelsexperiments as such presented as GSG in micromodelsthe work of Galindo based on-Rosales Bentheimer [61] and CT imagesScholz et [15,88,89], al. [59]. An completely overview imagetransparent of a GSG real micromodel porous-media as- resemblingused by Wegner plastic micromodelset al. [15], Rock (Hogeweg et al. [30], et al. Gaol2018) etand al. symmetric [89,90] and Hincapiemicromodels et al. [29]as presented as an example in the workis shown of Galindo by Figure-Rosales 13. In[61] addition, and Scholz valves et al. are [59]. installed An overview to allow evacuationimage of ofa GSGcertain micromodel parts of the as setup, used bye.g. Wegner, removing et al. gas [15], bubbles Rock inet theal. [30],pipes. Gaol Moreover, et al. [89,90] the syringe and pump,HincapiePolymers differential2020 et ,al.12, 2276[29] pressure as an example sensor, ismicroscope shown by Figureand camera 13. In addition,are connected valves to are a installedcomputer to18 enabling allow of 43 realevacuation-time monitoring of certain of parts the experiment. of the setup, e.g.The, removingremarkable gas advantages bubbles in the of thispipes. microfluidic Moreover, thesetup syringe are the pump, differential pressure sensor, microscope and camera are connected to a computer enabling low real-timerequired monitoringfluid volumes, of the good experiment. and fast Thepressure remarkable stabilization, advantages the ofopportunity this microfluidic of qualitative setup are flow real-time monitoring of the experiment. The remarkable advantages of this microfluidic setup are the assessment,the low requiredthe repr fluidoducibility volumes, of good results and and fast low pressure number stabilization, of connections the opportunity and parts of qualitativeresulting in a low required fluid volumes, good and fast pressure stabilization, the opportunity of qualitative flow reasonablyflow assessment, low fraction the reproducibility of failed experiments of results due and lowto setup number failure. of connections and parts resulting in a assessment, the reproducibility of results and low number of connections and parts resulting in a reasonably low fraction of failed experiments dueDifferential to setup Pressure failure.Sensor reasonably low fraction of failed experiments due to setup failure.

Differential Pressure Sensor Valve Valve

Valve Valve Syringe Pump

Micromodel Microscope Syringe Pump with Camera Microscope Valve Micromodel with Camera Valve

Computer Computer Effluent Collector Effluent Collector Figure 12. Microfluidic setup for quantitative and qualitative rheological measurements (modified afterFigureFigure [69]). 12. 12. MicrofluidicMicroﬂuidic setup setup for for quantitative and qualitativequalitative rheologicalrheological measurementsmeasurements (modiﬁed (modified afterafter [69] [69).]).

Figure 13. Glass-silicon-glass micromodel (40 40 0.05 mm) resembling the pore structure of Figure 13. Glass-silicon-glass micromodel (40 ×× 40 × 0.05 mm) resembling the pore structure of FigureBentheimer 13. Glass sandstone-silicon [30-glass]. micromodel (40 × 40 × 0.05 mm) resembling the pore structure of BentheimerBentheimer sandstone sandstone [30]. [30]. Another advantage of this type of micromodel setup is the easy experimental workflow for the diAnotherfferentAnother measurements, advantage advantage of of fromthis this type permeabilitytype of of micromodel micromodel measurements setup isis over thethe easy viscosityeasy experimental experimental evaluations workflow workflow to streamline for for the the differentdifferentvisualization. measurements, measurements, The basic from from polymer permeab permeab evaluationilityility measurementsmeasurements workflow using overover the viscosity setupviscosity presented evaluations evaluations above to consists tostreamline streamline of visualization.visualization.three steps: The The basic basic polymer polymer evaluation evaluation workflowworkflow usingusing thethe setup setup presented presented above above consists consists of of three steps: three(a) steps:Permeability measurement; (a) (a)Permeability(b) PermeabilityQuantitative measurement measurement polymer characterization; ; including viscosity evaluation; and (b) (b)Q(c) uantitativeQuantitativeA qualitative polymer polymer polymer characterization characterization characterization includingincluding including viscosity streamline ev evaluation visualization.aluation; and; and (c) A qualitative polymer characterization including streamline visualization. (c) A qualitativeThe latter polymer is explained characterization in detail in the including next section. streamline Each experiment visualization. starts with a permeability The latter is explained in detail in the next section. Each experiment starts with a permeability measurementThe latter is byexplained water flooding. in detail For in this, the the next experimental section. Each setup experiment is firstly flooded starts with with CO 2a inpermeability order to measurementguarantee a subsequent by water flooding. trouble-free For waterthis, the saturation experimental of the wholesetup is setup. firstly Once flooded the setup with isCO saturated2 in order measurement by water flooding. For this, the experimental setup is firstly flooded with CO2 in order to guarantee a subsequent trouble-free water saturation of the whole setup. Once the setup is to guaranteewith deionized a subsequent water, a visual trouble check-free of the water system saturation is performed of the in order whole to ensure setup. a Once gas bubble-free the setup is saturatedsystem, becausewith deionized these can water, cause a significant visual check differential of the system pressure is fluctuationsperformed in during order the to experiment.ensure a gas saturated with deionized water, a visual check of the system is performed in order to ensure a gas bubbleSubsequently,-free system, the micromodel because these is flooded can cause with significant deionized differential water at rates pressure ranging fluctuations from 100–700 duringµL/min the bubble-free system, because these can cause significant differential pressure fluctuations during the with flow rate increments of 100 µL/min. Each flooding step is 5 min long to ensure a stabilized differential pressure plateau. Afterwards, the differential pressure is used to calculate the permeability

using Darcy’s law. Overall, the average of all 7 ﬂooding steps is used for the ﬁnal permeability used for subsequent calculations in the quantitative polymer characterization. In addition to the permeability, Polymers 2020, 12, 2276 19 of 43

also the mean grain diameter Dp has to be determined in order to be able to calculate the Reynolds number given by: δfluid vs Dp Rem = (17) µapp(1 ε) − where δfluid is the fluid density, µapp the measured, apparent viscosity and ε the porosity [91]. Since the sandstone resembling micromodels usually do not consist of single, circle-shaped grains, it is not possible to determine Dp visually with an image algorithm. Therefore, Rock et al. [11] proposed the rearrangement of the Ergun equation [92] which is given by: q 2 2 2 2 4 2 3 1.75Lδfluid(1 ε)vs + 3.0625L δfluid (1 ε) vs + 600µL(1 ε) vs∆pε Dp = − − − (18) 2∆pε3 where L is the flow length along the micromodel, ∆p the measured differential pressure along the micromodel and µ the viscosity of the fluid. Since the viscosity of the viscoelastic polymer solutions change with different flow rates, it is necessary to determine Dp with the pressure data obtained during the permeability flooding with deionized water which is a Newtonian fluid and hence, has no viscosity changes with changing flow rates. After permeability and Dp measurements or rather calculations, the viscosity can be measured. For this purpose, the setup is completely saturated with the polymer solution which has to be rheologically characterized. Subsequently, the polymer is injected at different flow rates ranging from 0.25 µL/min up to 100 µL/min using the syringe pump. The differential pressure along the micromodel is measured each second in order to detect possible fluctuations which indicate problems with the experimental setup. Furthermore, it is highly recommended to use the automated injection function that most of the state-of-the-art syringe pumps offer. By that, an injection program can be set in the pump, so that the injection rate changes every 45 min. This allows the experiment to run overnight. Viscosity is determined by using the measured differential pressure and Darcy’s law. A typical apparent viscosity curve for a viscoelastic polymer solution injected in a GSG micromodel can be seen in Figure 11. The third step of the microfluidic polymer characterization is presented in the next section. The experimental approach presented above is similar to most of the setups found in literature and allows for many different modifications such as the addition of sensors, e.g., flow meter, absolute pressure sensors and gas sensors. The principle of a core flooding setup is basically the same as for the microfluidic flooding setup. The major differences are in the material (steel instead of plastic), the pump (higher injection pressures and volumes are required) and the differential pressure sensor. A schematic sketch of a core flooding setup for apparent viscosity measurements can be seen in Figure 14. Another major difference that can be seen in this setup is the pressurizing cylinder which is necessary in core flooding applications. An elastomer sleeve is put around the core plug, put in the Hassler cell and pressurized manually by adjusting the cylinder outside the cell [93–95]. By applying pressure around the sleeve, it is ensured that no injected fluid bypasses the core and, hence, distort, the measurement. As already mentioned in the explanation of the microfluidic setup, various kinds of modification can be added to the setup. The experimental workflow for single-phase polymer flooding using core plugs is basically the same as presented before for the micromodel experiments. Polymers 2020, 12, 2276 20 of 43 PolymersPolymers2020 2020,,12 12,, 2276 2276 2020 ofof 4343

Computer Computer

Differential Pressure Sensor

Multiple-Way Differential Pressure Sensor Valve Multiple-Way Elastomer Valve Sleeve Elastomer Sleeve Core Plug

Core Plug Hassler Cell Dual Syringe Pump Hassler Cell Dual Syringe Pump

Polymer CO Brine 2 Solution Pressurizing Polymer CO Brine Cylinder 2 Solution Pressurizing Cylinder Effluent Collector Effluent Collector Figure 14. Schematic sketch of a core floodingflooding setup used forfor experimentsexperiments at roomroom temperature.temperature. For experimentsFigure 14. Schematic at elevated sketch temperatures of a core thetheflooding HasslerHassler setup cellcell used andand inlet inlet/outletfor experiments/outlet pipespipes atareare room placedplaced temperature. inin anan oven.oven. For experiments at elevated temperatures the Hassler cell and inlet/outlet pipes are placed in an oven. Another approach for single-phasesingle-phase polymerpolymer flooding flooding in porous media is the use of a sand pack as porous Another media approach [96 [96––98]98 ]..for A A typicalsingle typical-phase sand sand packpo packlymer setup setup flooding can can be be seenin seen porous in inFigure Figuremedia 15 . 15 isInstead .the Instead use of of a of Hasslera sand a Hassler pack cell cellcontainingas porous containing mediaa core a core[96plug,–98] plug, a. cylinderA typical a cylinder filled sand filled with pack withsand setup sandis can used isbe used asseen porous asin porousFigure media. 15 media. .Thereby, Instead Thereby, of the a Hasslersand the h sandas cell a hasdefinedcontaining a defined grain a core grain diameter plug, diameter a which cylinder which allows filled allows for with for very sand very accurate is accurate used shearas shear porous rate rate media. calculations; calculations; Thereby, compared compared the sand to to h as the a defined grain diameter which allows for very accurate shear rate calculations; compared to the microfluidicmicrofluidic setup where Dp has to be calculated on the basis of the initial water flooding.flooding. Overall, themicrofluidic experimental setup workflowworkflow where D isisp thehasthe samesameto be asascalculated describeddescribed on forfor the micromodelmicromodel basis of the flooding.flooding. initial water flooding. Overall, the experimental workflow is the same as described for micromodel flooding.

Computer Computer

Multiple-Way Differential Valve Multiple-Way Pressure DifferentialSensor Valve Pressure Sensor

Dual Syringe Pump Dual Syringe Pump

Polymer CO Brine 2 Solution Polymer CO Brine 2 Solution Effluent Collector Effluent Collector Figure 15. Schematic sketch of a sand pack setup used for experiments at room temperature. For Figure 15. Schematic sketch of a sand pack setup used for experiments at room temperature. For experiments at elevated temperatures, the cell containing the sand and the inlet/outlet pipes needs are experimentsFigure 15. Schematic at elevated sketch temperatures, of a sand the pack cell setup containing used forthe experiments sand and the at inlet/outlet room temperature. pipes needs For placed in an oven. areexperiments placed in anat elevatedoven. temperatures, the cell containing the sand and the inlet/outlet pipes needs are placed in an oven. Other Viscoelastic Properties Other Viscoelastic Properties OtherIn Viscoelastic addition to Properties the relaxation time and shear viscosity of viscoelastic polymer solutions, the measurementIn addition to of the additional relaxation rheological time and parameters shear viscosity can be of used viscoelastic for further polymer fluid characterization solutions, the In addition to the relaxation time and shear viscosity of viscoelastic polymer solutions, the whichmeasurement improves of understanding additional rheological of polymer parameters structure can and be behavior. used for These further rheological fluid characterization parameters measurement of additional rheological parameters can be used for further fluid characterization includewhich improves first normal understanding stress difference of polymer as elastic st andructure viscous and modulus behavior. [37 These,99–101 rheological]. These are parameters commonly which improves understanding of polymer structure and behavior. These rheological parameters measuredinclude first by normal the use stress of state-of-the-art difference as elastic rotational and viscous rheometer, modulus but the [37,99 moduli,–101] for. These example, are commonly can also include first normal stress difference as elastic and viscous modulus [37,99–101]. These are commonly bemeasured measured by the using use theof state dynamic-of-the light-art rotational scattering rheometer, (DLS) technique but the developedmoduli, for byexample Duffy, etcan al. also [102 be] measured by the use of state-of-the-art rotational rheometer, but the moduli, for example, can also be andmeasured in detail using explained the dynamic by Hincapie light scattering [8]. For measurement (DLS) technique of extensional developed by viscosity, Duffy et the al. small [102] sample and in measured using the dynamic light scattering (DLS) technique developed by Duffy et al. [102] and in viscometerdetail explained (mVROC by ™ Hincapie) or the extensional [8]. For measurement viscometer-rheometer-on-a-chip of extensional viscosity, (eVROC the™ ) small as presented sample detail explained by Hincapie [8]. For measurement of extensional viscosity, the small sample byviscometer Pipe et al.(mVROC™) [103] and Elhajjajior the extensional et al. [65] canviscometer be used.-rheometer In this study,-on-a- basedchip (eVROC™) on the results as presented obtained viscometer (mVROC™) or the extensional viscometer-rheometer-on-a-chip (eVROC™) as presented fromby Pipe preliminary et al. [103] experiments and Elhajjaji prior et al. to [65] this can work, be itused is assumed. In this study, that the based extensional on the viscosity—oftenresults obtained by Pipe et al. [103] and Elhajjaji et al. [65] can be used. In this study, based on the results obtained discussedfrom preliminary as the additional experiments viscosity prior into shearthis work, thickening—is it is assumed notthe that reason the extensional for the viscosity viscosity increase—often in from preliminary experiments prior to this work, it is assumed that the extensional viscosity—often porousdiscussed media as the seen additional after the viscosity second criticalin shear shear thickening rate (see—is Sections not the 3.2.2reason and for 3.2.3 the ),viscosity but the increase onset of discussed as the additional viscosity in shear thickening—is not the reason for the viscosity increase elasticin porous turbulence. media seen This after is also the supportedsecond critical by the shear work rate of (see Howe Sections et al. [3.2.225]. Hence,and 3.2.3), its measurementbut the onset of is in porous media seen after the second critical shear rate (see Sections 3.2.2 and 3.2.3), but the onset of notelastic further turbulence. discussed This in is this also work. supported by the work of Howe et al. [25]. Hence, its measurement is notelastic further turbulence. discussed This in isthis also work. supported by the work of Howe et al. [25]. Hence, its measurement is not further discussed in this work.

Polymers 2020, 12, 2276 21 of 43

3.3.2. Qualitative Flow Evaluation Further enhancing state-of-the-art optical devices allows the flow of viscoelastic polymer solution in porous media to be characterized qualitatively. This provides additional data in order to understand the viscoelastic phenomena in porous media even better. One of the most important qualitative flow evaluations is the streamline visualization during flooding experiments. This is only possible if the porous media is transparent and, therefore, further underlines the advantage of the utilization of micromodels in the evaluation of viscoelastic polymer solutions used in EOR applications. In order to be able to see streamlines during the flow, tracer particles need to be added to the injected solution. The selection of tracer particles is a critical step in the streamline visualization process and, hence, requires a good understanding of the various types of particle offered. A first particle selection criterion is the particle size which is mainly dependent on the resolution and magnification the utilized optical setup offers. Rock et al. [30] and Sousa et al. [87] used microparticles with 1 µm diameter whereas Scholz et al. [59] used microparticles with diameters up to 3 µm. The smallest utilized particles utilized in literature were those of Galindo-Rosales et al. [104] with a diameter of 500 nm. Not only is the particle size a critical selection criterion from a setup point of view, but also from solution stability perspective. Sometimes prepared and well-mixed particle-polymer solutions are stored for later use. Therefore, using smaller particles is beneficial for solution stability since the particle settlement velocity in aqueous fluids is given by Stoke’s law [105]:

(δ δ ) 1 particle fluid 2 vsettlement = − g Dparticle (19) 18 µdynamic where vsettlement is the particle settlement velocity, δparticle the particle density, δfluid the fluid density, µdynamic the dynamic viscosity of the fluid, g the gravitational acceleration and Dparticle the particle diameter. As can be seen from the above equation, the particle diameter influences the velocity with which the particles settle to the bottom of the solution by the power of two. As an example, and assuming equal densities and dynamic viscosity, the particles used by Scholz et al. [59] settle 36 times faster than those used by Galindo-Rosales et al. [104]. It is important to note that the particles can also accumulate at the top of the prepared particle-polymer solution if δparticle is smaller than δfluid. Another important particle selection criterion is the chemical stability of the tracer particles. Using polymer solutions prepared with deionized water usually does not result in tracer stability problems. In contrast, using high salinity brine for the polymer solutions potentially causes stability problems which result in the formation of agglomerations which will accumulate at the bottom or the top (depending on the particle density) of the solution. Moreover, injection of these instable tracer particle can result in plugging of micromodels. Therefore, knowing the brine composition, salinity and also pH-value of the viscoelastic polymer solution is fundamental for the tracer selection process. In order to withstand harsh polymer solution properties, manufacturers usually offer different kinds of tracer surface modifications such as the addition of NH2-, COOH-, NR3-, SO3H-groups and many others which are not named due to their special use in medical and life science applications [106]. Sousa et al. [87] proposed the use of sodium dodecyl sulfate in order to stabilize the tracer particles further in the polymer solution, but this has to be evaluated for polymer solution separately since this can alter the fluid properties. Another selection criterion that has to be considered is the material of the tracer itself, not only due to the chemical interactions with the aqueous polymer solution but also due to the density. By that and regarding Equation (18), it is beneficial to choose tracer particles with a density close to that of the polymer solution in order to guarantee long-term stability. When choosing the tracer particle material, it is also important to consider the imaging method that will be used. If standard light microscopy is used it is recommended to use polystyrene particles as shown in the work of Hincapie et al. [29]. Rheological characterizations performed by Hincapie [8] on HPAM solutions showed viscosity alterations of approximately 1% and, thus, polystyrene particles are considered to be suitable for Polymers 2020, 12, 2276 22 of 43 qualitative flow evaluations of viscoelastic polymers. If fluorescence imaging technology is used, it is mandatoryPolymers 2020 to, 12 consider, 2276 the excitation and emission wave length of the particle to ensure that22 they of 43 are visualized by the optical setup. Otherwise, expensive filters and maybe even the light source of the are visualized by the optical setup. Otherwise, expensive filters and maybe even the light source of imaging setup needs to be changed. the imaging setup needs to be changed. Once the tracer particles are chosen and mixed into the aqueous polymer solutions, they can be Once the tracer particles are chosen and mixed into the aqueous polymer solutions, they can be injected into the transparent micromodels. The calibration of the imaging setup is different from case injected into the transparent micromodels. The calibration of the imaging setup is different from case to caseto case and and is is therefore therefore not not further further discussed discussed inin thisthis work. Examples Examples of of streamlin streamlinee visualizations visualizations are are shownshown in in Figures Figures6 and 6 and7. 7. ApartApart from from streamline streamline imaging imaging which which allows allows the qualitative description description of of viscoelastic viscoelastic flow flow phenomenaphenomena (e.g., (e.g. elastic, elastic turbulence), turbulence), the the tracer tracer particles particles can can also also be be used used for for a quantitativea quantitative in in situ situ flow characterizationflow characterization by velocimetry by velocimetry [55,59 ].[55,59]. InIn velocimetry, velocimetry stacks, stacks of imagesof images which which were were taken taken in short,in short, consecutive consecutive time time steps steps (<100 (<100 ms) ms) were used.were Thereby, used. Thereby, algorithms algorithm such ass thesuch PIVlab as the algorithm PIVlab algorithm in MATLAB in MATLAB™™ are used toare track used and to track analyze and the movementanalyze the of each movement particle of of each the flow. particle By definingof the flow. the By length defining of one the pixel length and of the one time pixel difference and the between time thedifference single images, between it is the possible single forimages, the algorithm it is possible to calculatefor the algorithm the velocity to calculate of each the particle velocity and of generate each anparticle overall and velocity generate map an of overall the flow. velocity An example map of the of suchflow. a An velocity example map of fromsuch a previous velocity experimentsmap from is shownprevious in experiments Figure 16. Although is shown in a timeFigure difference 16. Although of less a time than difference 100 ms between of less than consecutive 100 ms between images is required,consecutive 134 ms images is acceptable is required in, this134 ms case is dueacce toptable the lowin this flow case rate due of to 1 µthel/min. low flow Furthermore, rate of 1 µl/min. it is seen thatFurthermore, the scale bar it has is seen slightly that different the scale scaling bar has which slightly is different a problem scaling of the which software is a itself. problem The of results the obtainedsoftware from itself. velocimetry The results can obtained be used subsequentlyfrom velocimetry to calculate can be otherused subsequently flow properties to andcalculate also allow other for flow properties and also allow for a general analysis of the velocity distribution in the pore space. a general analysis of the velocity distribution in the pore space. Moreover, PIVlab offers various kinds of Moreover, PIVlab offers various kinds of analysis tools as the quantification of vorticity, shear rate, analysis tools as the quantification of vorticity, shear rate, x- and y-direction components of velocity and x- and y-direction components of velocity and averages. Additionally, distribution plots can be averages. Additionally, distribution plots can be generated in order to gain an even better overview and generated in order to gain an even better overview and understanding of the flow behavior of the understanding of the flow behavior of the polymer in the pore space. A remarkable disadvantage of polymer in the pore space. A remarkable disadvantage of velocimetry using particle tracing in velocimetry using particle tracing in micromodels is the resolution of tracers, especially at higher flow micromodels is the resolution of tracers, especially at higher flow rates. The higher the flow rate the rates.more The the higher tracer theparticles flow ratetend the to appear more the as tracera streamline. particles As tend a result, to appear the software as a streamline. cannot distinguish As a result, thethe software single particles cannot distinguish and is not able the singleto perform particles its analysis and is noton the able images. to perform In order its analysisto be able on to theperform images. In ordervelocimetry to be ablecharacterization to perform velocimetry even at high characterization flow rates, high- evenspeed at cameras high flow with rates, more high-speed than 500 frames cameras withper more second than are 500 required. frames per Generally, second are it canrequired. be stated Generally, that the it can quality be stated of results that the increase quality with of results an increaseincreasing with number an increasing of frames number per second of frames of the per camera. second of the camera.

FigureFigure 16. 16.Velocimetry Velocimetry analysis analysis forfor the flow flow of of a a 2000 2000 ppm ppm hydrolyzed hydrolyzed polyacrylamide polyacrylamide (HPAM (HPAM)) at 1 at 1 µµL/minL/minflow flow raterate inin aa porous-media-resemblingporous-media-resembling micromodel micromodel performed performed with with PIVlab PIVlab in inMATLAB™. MATLAB ™. TheThe input input images images for for each each velocimetry velocimetry image image werewere takentaken with 134 ms ms time time difference. difference.

Polymers 2020, 12, 2276 23 of 43 Polymers 2020, 12, 2276 23 of 43

Another qualitative flowflow evaluation method that was published in literature recently was thethe use ofof X-rayX-ray imagingimaging onon realreal sandstones.sandstones. Vik et al. [[107]107] presentedpresented this flowflow imagingimaging approachapproach inin detail. X X-ray-ray imaging in sandstone samples require a special preparation of thethe rock.rock. First, the rocks werewere cutcut inin quadraticquadratic slabsslabs whichwhich werewere subsequentlysubsequently coatedcoated withwith epoxy.epoxy. Afterwards,Afterwards, thethe sandstonesandstone slabs were measuredmeasured forfor porosity and permeability, saturatedsaturated withwith oil,oil, andand agedaged atat 5050 ◦°C,C, over three weeks.weeks. Following Following the the ageing ageing process, process, the the sandstone sandstone slab slab was saturated with the oil used in the the experiment. Subsequently, Subsequently, the the sample sample was was put put into into a 2D a X-ray 2D X scanner-ray scanner which which had a low-energyhad a low-energy source andsource NaI and detector. NaI detector. The researchers The resear statechers that the state minimum that the time minimum for one X-raytime for image one was X-ray approximately image was 5approximately min which should 5 min notwhich be exceededshould not in be order exceeded to visualize in order the to visualize dynamic the flow. dynamic The result flow. of The the result flow visualizationof the flow visualization can be seen incan Figure be seen 17. in It canFigure be seen17. It that can X-ray be seen imaging that X is-ray capable imaging of visualizing is capable the of displacementvisualizing the process displacement in two-phase process polymer in two- floodingphase polymer experiments flooding at aexperiments remarkably at high a remarkably resolution. Thereby,high resolution. this technology Thereby, providesthis technology a significant provides contribution a significant in contribution the understanding in the understanding of displacement of processesdisplacement by viscoelastic processes by properties viscoelastic and, properties hence, it should and, he bence, considered it should as be a considered powerful tool as ina powerful polymer flowtool in characterization. polymer flow characterization. Nevertheless, this Nevertheless, visualization this method visualization requires expensivemethod requires equipment expensive which additionallyequipment which requires additionally well-trained requires scientific well sta-trainedff to operate scientific it. staff to operate it.

Figure 17. Two-dimensional (2D) X-ray images of oil displacement in sandstone slabs using HPAM, HPAM-S,Figure 17. glycerol, Two-dimensional xanthan and (2D water) X-ray at ratesimages varying of oil displacement between 0.3 and in sandstone 0.8 mL/min, slabs equaling using a HPAM, typical reservoirHPAM-S, rate glycerol, of 0.3 xanthan m/day. [ 107and]. water at rates varying between 0.3 and 0.8 mL/min, equaling a typical reservoir rate of 0.3 m/day. [107]. 3.4. Impacts on Polymer Viscoelasticity in Oil Reservoirs 3.4. Impacts on Polymer Viscoelasticity in Oil Reservoirs During the preparation, injection and displacement in oil reservoirs, viscoelastic polymer solutions experienceDuring a broad the preparation, range of di ff injectionerent potential and displacement impacts on their in oil viscoelasticity reservoirs, viscoelastic and thereby polymer on their overallsolutions performance experience ina broad EOR applications.range of different Influencing potential fluid impacts properties on their like viscoelasticity solvent salinity, and polymer thereby concentrationon their overall and performance molecular weightin EOR alter applications. the in situ Influenc rheologying of fluid the polymerproperties solution. like solvent Furthermore, salinity, reservoirpolymer concentrationrock characteristics and molecular and the related weight mechanical alter the in stress situ have rheology impact of theas well. polymer Additionally, solution. Furthermore, reservoir rock characteristics and the related mechanical stress have impact as well. Additionally, thermal degradation, chemical alterations and biological degradation by bacteria

Polymers 2020, 12, 2276 24 of 43 thermal degradation, chemical alterations and biological degradation by bacteria significantly influence the polymer’s rheology and, therefore, must be studied and understood in order to account for these impacts. Knowledge of potential degradation mechanisms results in an improved polymer optimization and, possibly, results in higher displacement efficiencies.

3.4.1. Solvent Salinity A big disadvantage of viscoelastic HPAM polymers is their sensitivity to salinity of the solution which is reflected as a decreased viscosity and relaxation time [10,18,108–111]. Abidin et al. [18] studied that the main reason behind the decrease of relaxation time and viscosity of HPAM polymers in high-salinity environments are the divalent cations that connect to the acrylate parts of the polymer chains. Moreover, these researchers have shown that divalent cations such as Ca2+ and Mg2+ have a significantly stronger impact than monovalent cations such as Na+ and K+. This indicates a correlation between cation type and degree of relaxation time decrease. In contrast to this, most of the literature as presented for example in Turkoz et al. [109] assumes that the charge-screening effect is the main driver of relaxation time reduction and therefore, it only depends on salt concentration. The charge-screening mechanism is described by Sasaki [112] as the effect of external charges (cations of the salt) partially bonding to the molecule which are then screened by internal electrons. As a result, the charge of the polymer molecule alters to an electronically neutral state yielding a reduction of the polymer’s viscoelasticity. Although salt concentration is assumed to be the most significant reason for viscoelasticity reduction due to solution salinity, Turkoz et al. [109] investigated the effect of different cation types, e.g., NaCl, C7H5NaO3, KCl, CsCl, CaCl2 and ZnCl2. In contradiction to the previous findings of Abidin et al. [18] claiming a remarkably stronger relaxation time reduction for divalent cations, Turkoz et al. [109] observed no significant differences between monovalent and divalent cations. The authors give a potential explanation for the results obtained by Abidin et al. [18]. During their experiment they observed a distinct pH value decrease for polymer solutions with salts of divalent cations. Therefore, they underline that the results of salinity studies have to be analyzed carefully and critically since pH value alteration is another polymer degradation mechanism. pH-value alteration and its effect on polymer viscoelasticity is discussed in detail later. The researchers assume a correlation between polymer solubility and the Hofmeister series [113] which is defined as follows:

Cs+ > K+ > Na+ > Ca2+ > Zn2+ (20)

According to Turkoz et al. [109], the polymer solubility increases to the right of the series and thereby decreases the viscoelasticity. However, the researchers proved that this is only valid for monovalent cations and not for divalent cations. Additionally, they relativize their findings with another correlation they have observed during their rheology measurements. It is seen that the relaxation time alteration can be correlated to the ionic radius of the monovalent cations. Hereby, the larger the ionic radius of the monovalent cations, the stronger is the reduction in the relaxation time of the polymer solution. These researchers have also shown that the ionic radius of the anions has no effect on the polymer’s viscoelasticity. For divalent cations, Turkoz et al. [109] have shown that the hydrated radius of divalent salts has an influence on the relaxation time alteration. Hereby, the effect on the viscoelasticity is more distinctive for larger hydrated radii. In conclusion, it can be summarized that with an increasing salinity of the polymer solution and depending on the anion composition of the solution, the viscosity and relaxation time is decreased and, therefore, will have an effect on the polymer flooding efficiency in the oil field. The decrease of viscosity and relaxation time for HPAM polymers have been experimentally shown in preliminary experiments of Rock [69]. Exemplary results are shown in Figure 18. As it can be seen the viscosity of the aqueous polymer solution with 0.4 g/L TDS is significantly higher than the one measured for the solution with 4.0 g/L Polymers 2020, 12, 2276 25 of 43

TDS. Furthermore, the onset for the polymer solution with lower salinity starts at lower shear rates thanPolymers for 2020 the, one12, 2276 with higher salinity. This is a strong indication of a stronger viscoelastic response25 of of the 43 low-salinity polymer solution. This result is conﬁrmed by relaxation time measurements performed usingperformed a rotational using rheometer.a rotational The rheometer. results are The shown results in Tableare shown2. The in relaxation Table 2. timesThe relaxation for the low times salinity for polymerthe low salinity solution polymer are more solution than 10 are times more higher than than10 times for the higher high than salinity for solution.the high s Foralinity the 500solution. ppm 4For g/ Lthe TDS 500 polymer ppm 4 g/L solution TDS polymer it was not solution possible it towas measure not possible the relaxation to measure time the due relaxation to its low time value. due to its low value.

Figure 18. ApparentApparent viscosity viscosity measured measured during during micromodel micromodel flooding flooding plotted plotted against against shear shear rate. rate. Yellow trianglestriangles markmark the onset of the transitional flow-regimeflow-regime and blue triangles the onset of elastic turbulence. [[69].69]. Table 2. Relaxation times of HPAM polymers with different solution salinity and polymer Table 2. Relaxation times of HPAM polymers with different solution salinity and polymer concentrations [69]. concentrations [69]. Polymer Concentration, Solution Salinity Molecular Weight, Relaxation Time, Polymer Concentration,c [ppm] c Solution[g/l TDS] Salinity MolecularMW [MDa] Weight, Relaxationλ [s] Time, [ppm] [g/l TDS] MW [MDa] λ [s] 500 4.0 29 n.a. 500 4.0 29 n.a. 1000 4.0 29 2.31 1000 4.0 29 2.31 15001500 4.04.0 2929 3.333.33 500500 0.40.4 2929 17.2217.22 10001000 0.40.4 2929 25.6225.62 15001500 0.40.4 2929 40.9340.93

3.4.2. Polymer Concentration Polymer concentration concentration is isthe the most most critical critical factor factor influencing influencing the viscoelastic the viscoelastic of polymer of solutions. polymer Generally,solutions. Generally, an increase an of increase the polymer of the concentration polymer concentration results in an results increase in ofan viscoelasticity increase of viscoelasticity as well as of viscosity.as well as Thisof viscosity. behavior This is proved behavior by ais broadproved range by a ofbroad literature range such of literature as the advanced such as the experimental advanced worksexperimental of Howe works et al. of [25 Howe], Clarke et al. et [25], al. [55 Clarke], Hincapie et al. [55], [8], RockHincapie et al. [8], [30 ],Rock Heemskerk et al. [30], [114 Heemskerk], Tahir et al.[114], [84 ]Tahir and Serightet al. [84] et al.and [115 Seright]. et al. [115]. The eeffectffect ofof polymerpolymer concentrationconcentration on the viscoelasticity is illustrated in Figure 1919.. As can be seen from the plot, plot, the the viscosity viscosity increases increases with with an an increasing increasing polymer polymer concentration. concentration. Furthermore, Furthermore, it ithas has be be noted noted that that the the increase increase seems seems to tobe benon non-linear.-linear. Additionally, Additionally, the the decreasing decreasing onset onset shear shear rate rate of ofthe the transition transitionalal and and turbulent turbulent flow flow regime regime indicate indicate an an increasing increasing viscoelasticity viscoelasticity of of the polymer solutions. This is further underlined by measured relaxation times [69]. In core flooding experiments, solutions. This is further underlined by measured relaxation times [69]. In core flooding experiments, an increasing viscoelasticity is observed as wellwell forfor anan increasingincreasing polymerpolymer concentrationconcentration [[60].60].

Polymers 2020, 12, 2276 26 of 43 Polymers 2020, 12, 2276 26 of 43

FigureFigure 19.19. ApparentApparent viscosityviscosity ofof HPAMHPAM solutionssolutions withwith didifferentfferent polymerpolymer concentrationsconcentrations measuredmeasured duringduring micromodelmicromodel single-phasesingle-phase flooding. flooding. YellowYellow triangles triangles mark mark thethe onsetonset ofof transitionaltransitional flowflow regimeregime and blue triangles mark the onset of fully developed elastic turbulence [69]. and blue triangles mark the onset of fully developed elastic turbulence [69]. 3.4.3. Molecular Weight 3.4.3. Molecular Weight The molecular weight Mw of viscoelastic polymer solutions has a large influence on the polymer floodThe efficiency molecular since weight its impact Mw on of theviscoelastic viscoelasticity polymer is significant.solutions has Thereby, a large usinginfluence high on Mw the polymers polymer canflood significantly efficiency since enhance its impact the EOR on projects’the viscoelasticity economics is [significant.16]. Thereby, using high Mw polymers can significantlyThe impact of enhance Mw on the the EOR polymer projects’ solutions economics viscoelasticity [16]. is the result of intramolecular effects, especiallyThe impact energetic of Mw and on steric the polymer interactions solutions of chains viscoelasticity within the is the polymer result of molecule. intramolecular Specifically, effects, theespecially amino groupsenergetic of polymersand steric showinteractions these interactions of chains within which the result polymer in an increasemolecule. of Specifically, relaxation time the asamino well groups as of viscosity. of polymers Additionally, show these long interactions polymer which chains, result hence in high an increase Mw polymers, of relaxation have time both as a significantwell as of advantage viscosity. and Additionally, disadvantage long regarding polymer the chains, viscoelasticity. hence high The Mw advantage polymers, on the have one both hand a issignificant the enhancing advantage degree and of disadvantage polymer chain regard overlappinging the viscoelasticity. resulting in an The earlier advantage onset of on polymer the one hand flow instabilities.is the enhancing On the degree other of hand, polymer it is achain remarkable overlapping disadvantage resulting that in an polymer earlier solubilityonset of polymer is decreased flow withinstabilities. an increasing On the Mw. other Therefore, hand, it isa a compromiseremarkable disadvantage needs to be defined that polymer which solubility again underlines is decreased the with an increasing Mw. Therefore, a compromise needs to be defined which again underlines the necessity and benefit of experimental fluid optimization prior to the field application [116]. necessity and benefit of experimental fluid optimization prior to the field application [116]. Choosing a viscoelastic polymer with a suitable Mw requires accounting for two main Choosing a viscoelastic polymer with a suitable Mw requires accounting for two main considerations. First, a polymer with the highest possible Mw has to be selected in order to increase or considerations. First, a polymer with the highest possible Mw has to be selected in order to increase rather maximize the viscoelastic response of the polymer solution and, therefore, reduce the amount or rather maximize the viscoelastic response of the polymer solution and, therefore, reduce the of polymer required. Second, the pore size distribution of the reservoir rock needs to be considered amount of polymer required. Second, the pore size distribution of the reservoir rock needs to be in order to ensure a sufficient propagation of the injected polymer solution through the reservoir, considered in order to ensure a sufficient propagation of the injected polymer solution through the otherwise pore plugging can occur and decrease the displacement efficiency. These two considerations reservoir, otherwise pore plugging can occur and decrease the displacement efficiency. These two can be translated into a simple equation based on empirical evaluations performed on the polymer considerations can be translated into a simple equation based on empirical evaluations performed on EOR projects of the Daqing oil field in China. It is given by: the polymer EOR projects of the Daqing oil field in China. It is given by: 13 Mw,max = 11.111 9.86923 10−−13 kwater + 0.005 (21) 푀푤,푚푎푥 = 11.111 (9.86923∗∗ 10 ∗ ∗ 푘푤푎푡푒푟 + 0.005) (21)

2 2 wherewhere MMw,w, max max is isthe the maximum maximum Mw Minw MDain MDa and k andwater isk waterthe wateris the permeability water permeability in m . Another in m .correlation Another correlationthat can be thatused can for be selection used for of selection a proper of maximum a proper maximumMw is the followingMw is the ratio following: ratio:

퐴푣푒푟푎푔푒Average 푃표푟푒 Pore 푇 Throatℎ푟표푎푡 Radius 푅푎푑𝑖푢푠 > 5 > 5 ( (22)22) 푅표표푡Root 푀푒푎푛 Mean 푆푞푢푎푟푒 Square 푅푎푑𝑖푢푠 Radius o표푓 fPolymer 푃표푙푦푚푒푟 Gyration 퐺푦푟푎푡𝑖표푛

Both guidelines yield to the approximately same result that for reservoirs with an average permeability larger 1000 mD a polymer with a Mw of 12–16 MDa should be used and a polymer with a Mw of 17–25 MDa should be selected for permeability larger than 4000 mD. [116].

Polymers 2020, 12, 2276 27 of 43

3.4.4. Mechanical Degradation Mechanical degradation can be understood as the break-up of polymer chains or rather molecules due to mechanical forces caused by the high shear stress [13,17,43,70,71]. Usually those conditions are encountered in the near-wellbore region and in the equipment such as pumps and valves. The effect decreasing the viscoelastic properties as well as the viscosity of the mechanically degraded polymer solutions is the lower Mw of the polymer chains due to the molecular rupture of them [117]. Furthermore, these researchers showed that the polymer chains break when they are stretched in an entanglement system. This assumption is supported by the work from Bueche [118]. Larsen and Drickamer [119] mention in their work that polymer molecules most likely break at the C–C bonds. Bueche [118] discusses the way polymer molecules break up due to mechanical degradation. Firstly, it was assumed that polymer chains break up because of extensive stretching to a point where the stretching force overcomes the bonding force. However, Bueche [118] explains that even at high shear rates the degree of stretching is too low to explain the degradation. A more advanced explanation for the break up is that the polymer rotates significantly fast, so that it is not considerably stretched. As a result, the distortion of the polymer molecule increases which yields to break at a certain point. A further mechanism of mechanical degradation explained by Bueche [118] is related to the entanglement of polymer molecules, as already mentioned before. At high shear rates, the degree of entanglement is increased which induce tensional stresses to the molecules in the center of entanglement networks. In addition to the literature presented above, Frenkel [120] found that the probability of breaking is the highest in the center of the polymer molecule. In order to avoid any pre-shearing and, therefore, mechanical degradation of the polymer in the surface equipment in the field, Sheng et al. [17] propose to use electromagnetic flowmeters.

3.4.5. Thermal Degradation A disadvantage of viscoelastic HPAM polymers is their thermal sensitivity [121–123]. The acrylamide groups of the polymer start to hydrolyze at 60 ◦C resulting in sodium acrylate. This yields precipitation and, therefore, a loss of relaxation time and viscosity [124]. This mechanism of thermal polymer degradation is also described by Levitt and Pope [10]. These researchers see the rupture of the acrylic group as the cause of relaxation time and viscosity loss by the reduction of Mw. The reason for the breakdown of the acrylamide groups are free radicals. Regarding the thermal degradation of polymers, carbon-centered radicals are of particular importance and only form when polymerization initiators are thermally decomposed. These radicals are able to abstract hydrogen from the polymer molecule, at least from its backbones. Nevertheless, this process requires oxygen and is therefore strongly limited in the reservoir. Levitt and Pope [10] also state that the presence of iron is enough as well for the radicals to hydrolyze the acrylic groups. Another explanation for thermal polymer degradation is given by Maurer and Harvey [121]. These researchers describe thermal degradation in terms of ammonia loss. At elevated temperatures the polymer molecule loses ammonia resulting in the formation of imide which is subsequently decomposed. By that, the polymer loses Mw and finally, viscosity and relaxation time. The reservoir temperature impact on the viscoelastic behavior of the polymer solution is critical and, therefore, has to be considered in the EOR selection and designing process. Different recommendations for maximum reservoir temperatures are given in Table3. As it is seen, the highest temperature is the one proposed by Saleh et al. [125], whereas the lowest one is proposed by Saboorian-Joybari [126]. The differences within the literature are the result of the many other criteria which were considered. For example, if a reference recommends a lower temperature, this could be due to a high polymer Polymers 2020, 12, 2276 28 of 43 solution salinity. Therefore, the maximum allowable temperature is reduced to account for the degradation effects of the salinity.

Table 3. Literature recommended maximum reservoir temperatures for polymer ﬂooding in oil reservoirs (modiﬁed after [35]).

Reference Recommended Maximum Reservoir Temperature [◦C] Taber et al. (1997) <93 Saleh et al. (2014) <99 Dickson et al. (2010) <77 Delamaide et al. (2016) <80 Saboorian-Joybari (2015) <65

3.4.6. Chemical Degradation Apart from mechanical and thermal degradation in the reservoir, the polymer also faces chemical degradation [127,128], mainly due to further hydrolysis of its molecules. Hydrolysis of polymers in the reservoir is dependent on the pH-value of the reservoir brine. For smaller polymer molecules, mainly the amide groups are hydrolyzed either by a basic or acidic hydrolysis. Thereby, small molecules are sensitive to low as well as to high pH values. In the case of larger polymer molecules, intermolecular effects can become important, which either accelerate or decelerate the hydrolysis of the polymer in the reservoir. Levitt and Pope [10] state that an acceleration is usually observed at low pH values, whereas high pH values retard the hydrolysis. For this reason, polymers in basic environments usually do not exceed a hydrolysis degree of 66%. The problem of a too high hydrolysis degree is as follows: HPAMs with a hydrolyzed fraction of 33% or higher often encounter chemical stability problems (precipitation) when the solution contains a large number of divalent cations such as Ca2+ and Mg2+. This issue becomes more severe with an increasing temperature. This perfectly illustrates interactions of different degradation effects/mechanisms [10]. A further problem regarding the chemical degradation of polymers is the oxidation of its molecule by oxygen or rather free radicals, as already explained in Section 3.4.6. Therefore, polymer EOR projects often require the utilization of oxygen scavengers such as hydrazine, sodium bisulfite, sodium hydrosulfite or sulphur dioxide [129]. Overall, chemical degradation resulting from further hydrolysis and oxidation causes a Mw loss and, therefore, yields to a decreased viscoelasticity.

3.4.7. Biological Degradation Biological degradation usually refers to biopolymers such as xanthan gum since these types of polymer are polysaccharides which are a favorable source for bacteria growth. Nevertheless, studies have shown that a small number of sulphate-reducing bacteria (SRB) is able to use viscoelastic HPAM as a source for metabolism [17]. Jia et al. [130] reports that SRB uses HPAM as a source for carbon. Mainly the amide and carbon-containing backbones of the HPAM are used, whereas the amide is an additional source for nitrogen. As a result of the SRBs degrading the HPAM, the polymer chains are broken up resulting in a loss of viscoelasticity by molecular weight reduction. Although there is only a very small number of SRBs able to degrade viscoelastic HPAMs, researchers were able to identify them. Jia et al. [130] states that mainly B. cereus biologically degrades the HPAM, whereas Al-Moqbali et al. [131] reports T. mobilis, P. aeruginosa as well as P. stutzeri to be the problematic SRBs. Here, it is important to note that Jia et al. [130] mainly refers to oﬀshore polymer ﬂooding projects where sea water can be seen as an additional source for bacteria in the reservoir. This has to be seen as critical since sea water bacteria are aerobic. The bacteria named by Polymers 2020, 12, 2276 29 of 43

Al-Moqbali et al. [131] are aerobic and hence are not further considered to degrade the HPAM in the reservoir. Nevertheless, when mixed in bulk on the surface, biodegradation resulting from these bacteria can occur. Apart from reducing the molecular weight and, therefore, viscoelasticity of the polymer solution, SRBs are able to form hydrogen sulﬁde (H2S) resulting in reservoir damage due to souring. Therefore, Sheng et al. [17] recommends the use of biocides such as formaldehyde in order to avoid this kind of biological degradation and for avoidance of reservoir damage.

3.4.8. Impact of Reservoir Rock on the Viscoelastic Flow Behavior The impact of reservoir rock has no directly related effect on the viscoelasticity of the polymer solution. However, in the authors’ opinion, it is important to mention the fundamental polymer–solid interactions affecting the overall field application efficiency. First of all, it has to be stated that polymer flooding is usually applied to sandstone reservoirs and not to carbonate reservoirs. In the latter case, carbonates have a high ionic exchange capacity and low permeability (in the matrix) and, therefore, the polymer shows a high adsorption or strong plugging respectively [17,132]. Considering the effect of the reservoir rock on the polymers’ performance, the most important terms are adsorption and retention. Polymer adsorption means that during the flow of HPAMs the polymer molecules tend to adhere to the surface of the rock. This adsorption takes place until a complete one layer adsorption is reached which results in an irreversible polymer coverage of the reservoir rock. Furthermore, adsorption is faster for polymers with higher molecular weight. As a result of polymer adsorption, polymer solution loses 4–30% pore volume (PV). The broad range of polymer loss is the result of varying temperature and salinity [116]. The high polymer losses can not only be explained with adsorption since adsorption happens only until full surface coverage of the rock and there is no polymer-on-polymer adsorption. Hence, retention effects are considered to be responsible for polymer losses in the reservoir. These effects are mainly dependent on the polymer concentration in the injection solution and on brine salinity. Thereby, the polymer retention volume increases with increasing concentration and salinity [116]. The resistance factor RF of the reservoir rock increases during polymer flooding. The resistance factor is generally defined as: kw µ RF = w (23) kp µp where kp is the relative permeability of the polymer solution and µp the polymer viscosity [13,115]. Seright et al. [13] reported increasing resistance factors for xanthan floods in Berea cores. Assuming constant permeability, only the viscosity affects RF and therefore, an increasing RF is the result of the higher polymer viscosity. More realistically, an increasing resistance factor in reservoir has a two-folded effect: on the one hand, the increasing resistance factor—a synonym for pore plugging—has a beneficial effect in high permeability zones by improving the sweep efficiency. On the other hand, an increased resistance factor means an irreversible permeability reduction which can have a negative effect on subsequent floods. This is referred to as residual resistance factor (RRF):

k RRF = 2 (24) k1 where k2 is the reservoir brine permeability after and k1 before the polymer ﬂooding. Thus, an increasing RRF is the result of a permeability reduction. It is important to note that polymers and especially HPAMs lose their ability of pore plugging when undergoing mechanical degradation [133]. For a proper injectivity, Hincapie [69] proposes a RRF below 3. Polymers 2020, 12, 2276 30 of 43

Kolnes and Nilsson [132] also discuss the rock-related influence on the polymer behavior from a Polymersgeochemical 2020, 12/lithological, 2276 perspective. These researchers highly emphasize the value of knowledge30 of of43 the rock composition. Thereby, three main geochemical or rather lithological factors are important: exchange capacity and by that, it influences the polymer retention. Therefore, the polymer retention (1) the presence of CaMg(CO ) and CaCO (carbonates), (2) FeCO and (3) clay content. The presence increases with an increasing 3clay2 content. 3Apart from the clay fraction3 in the rock, also the clay type of carbonates strongly controls the pH-value and hence, its viscoelasticity. Furthermore, FeCO is from a significant importance. Austad et al. [134] report the highest cation exchange capacity for3 affects the polymer’s stability. The clay content of reservoir rock is important in terms of cationic Montmorillonite (80–150 meq/100g) whereas the lowest is related to kaolinite (3–15 meq/100g). exchange capacity and by that, it influences the polymer retention. Therefore, the polymer retention According to this study, a remarkably higher polymer retention is expected for a sandstone increases with an increasing clay content. Apart from the clay fraction in the rock, also the clay containing montmorillonite rather than kaolinite. type is from a significant importance. Austad et al. [134] report the highest cation exchange capacity for Montmorillonite (80–150 meq/100 g) whereas the lowest is related to kaolinite (3–15 meq/100 g). 4. Viscoelasticity-Related Recovery Mechanisms and Their Importance in EOR Applications According to this study, a remarkably higher polymer retention is expected for a sandstone containing montmorilloniteThis section rather focuses than specifically kaolinite. on the recovery mechanisms resulting from polymer viscoelasticity. Therefore, mechanisms such as reduction of viscous fingering are not discussed. Sheng4. Viscoelasticity-Related et al. [17] state four Recovery main recovery Mechanisms mechanisms and Their resulting Importance from polymer in EOR Applications viscoelasticity: (1) pullingThis mechanism, section focuses (2) oil specifically-thread flow, on the (3) recovery stripping mechanisms mechanism resulting, and (4) fromshear polymer thickening. viscoelasticity. Therefore,The pulling mechanisms mechanism such can as reductionbe understood of viscous as a pull fingering-out of areoil trapped not discussed. in dead Sheng-end pores. et al. The [17] oilstate-thread four mainflow becomes recovery especially mechanisms important resulting after from wat polymerer flooding viscoelasticity: where the (1)residual pulling oil mechanism, is divided into(2) oil-thread single drops. flow, Due(3) stripping to the injection mechanism, of viscoelastic and (4) shear polymer thickening. solutions, the oil drops are pulled togetherThe topulling oil threads. mechanism These can threads be understood allow the as oil a pull-out to flow of towards oil trapped the residual in dead-end oil located pores. downstreamThe oil-thread and flow thus, becomes results especially in the formation important of after an oil water bank flooding which can where be recovered the residual more oil is easily. divided intoAs single can drops.be seen Duein Figure to the 20 injectiona the oil is of left viscoelastic behind as polymer isolated solutions,oil drops after the oilwater drops flooding. are pulled Due totogether the injection to oil threads. of viscoelastic These threads polymer allow solution the oil in to Figure flow towards20b, these the dro residualps are oilstretched located and downstream thinned resultingand thus, in results the formation in the formation of an oil of thread an oil in bank the whichpore space. can be Along recovered this oil more thread, easily. the polymer drops flow Asand can form be seenan oil in bank Figure downstream 20a the oil iswhich left behind is easier as to isolated recover oil than drops single after oil water droplets flooding. trapped Due in to the pore injection structure. of viscoelastic Note that polymer the oil thread solution viewpoint in Figure(a) of 20 viscoelasticb, these drops polymer are stretchedflooding may and thinnedbe only suitableresulting for in theexplaining formation the of large an oil-sized thread pores in thebut pore not space.small-sized Along pores this oilor thread,nano-/micro the polymer-meter pores. drops Furtherflow and research form an is oil required bank downstream is this direction. which is easier to recover than single oil droplets trapped in the poreAnother structure. mechanism Note thatdescribed the oil by thread Sheng viewpoint et al. [17] of is viscoelastic the stripping polymer mechanism. flooding As maythe name be only of thesuitable mechanism for explaining indicates, the the large-sized oil on the porespore walls but not is stripped small-sized off. The pores researchers or nano-/ micro-meterexplain this by pores. the higherFurther velocity research of is the required viscoelastic is this polymer direction. solution at the pore walls.

(a) (b)

Figure 20. (a) Situation after conventional water flooding. The oil is left as isolated oil drops; Figure 20. (a) Situation after conventional water flooding. The oil is left as isolated oil drops.; (b) (b) viscoelastic polymer solution is injected resulting in the formation of an oil thread along which the viscoelastic(b) polymer solution is injected resulting in the formation of an oil thread along which the oil oil upstream flows along and build-up an oil bank downstream. upstream flows along and build-up an oil bank downstream. Another mechanism described by Sheng et al. [17] is the stripping mechanism. As the name of The fourth mechanism mentioned by Sheng et al. [17] is the shear thickening which is assumed the mechanism indicates, the oil on the pore walls is stripped off. The researchers explain this by the to increase the viscosity as a result of the viscoelasticity. As already discussed in detail, this study higher velocity of the viscoelastic polymer solution at the pore walls. does not assume an actual viscosity increase of the injected polymer, but an additional pressure drop The fourth mechanism mentioned by Sheng et al. [17] is the shear thickening which is assumed to caused by the elastic turbulence. Evidence for this assumption is given by the studies of Hincapie et increase the viscosity as a result of the viscoelasticity. As already discussed in detail, this study does al. [29] and Rock et al. [11]. These researchers have clearly shown that viscoelasticity is capable of not assume an actual viscosity increase of the injected polymer, but an additional pressure drop caused increasing the oil recovery by viscoelastic effects, mainly elastic turbulence. by the elastic turbulence. Evidence for this assumption is given by the studies of Hincapie et al. [29] Figures 21 and 22 show the experimental results of Rock et al. [11]. In Figure 21 the results for and Rock et al. [11]. These researchers have clearly shown that viscoelasticity is capable of increasing the laminar flow regime can be seen. On the left side (red) the initial oil saturation is shown which the oil recovery by viscoelastic effects, mainly elastic turbulence. was quantified by using a MATLAB® algorithm. The initial oil saturations (Soi) for pores 1 to 5 were 97.94%, 95.21%, 90.07%, 86.18% and 84.30%. After Soi was determined, non-viscoelastic polyethylene oxide (PEO) were injected (0.5 µL/min) in order to displace the oil without any viscoelastic effects. The residual oil saturations (Sor) after PEO flooding from pores 1 to 5 were 97.94%, 0.00%, 90.07%, 34.64% and 20.18% respectively. Therefore, as can be seen there are some pores where all the oil was

Polymers 2020, 12, 2276 31 of 43

Figures 21 and 22 show the experimental results of Rock et al. [11]. In Figure 21 the results for the laminar flow regime can be seen. On the left side (red) the initial oil saturation is shown which ® was quantified by using a MATLAB algorithm. The initial oil saturations (Soi) for pores 1 to 5 were 97.94%, 95.21%, 90.07%, 86.18% and 84.30%. After Soi was determined, non-viscoelastic polyethylene oxide (PEO) were injected (0.5 µL/min) in order to displace the oil without any viscoelastic effects. The residual oil saturations (Sor) after PEO flooding from pores 1 to 5 were 97.94%, 0.00%, 90.07%, 34.64% and 20.18% respectively. Therefore, as can be seen there are some pores where all the oil was recovered and some pores where no oil was displaced. In order to see the influence of viscoelastic recovery mechanisms at a laminar flow regime, a 500 ppm polymer solution which has the same viscosity as the previously injected 3350 ppm PEO solution was injected (0.5 µL/min). Sor after the flood for pores 1 to 5 had determined to be 97.94%, 0.00%, 90.07%, 37.19% and 0.00%. Overall, the additional recovery was 4.43% due to viscoelastic effects from the injected HPAM. In order to determine the recovery efficiency of elastic turbulence, Rock et al. [11] performed the same experiment for a higher flow rate to create elastic turbulence in the porous-media resembling a GSG micromodel. The qualitative results from streamline visualization are seen in Figure 22. The initial oil saturations were determined for pores 1 to 5 to be 93.87%, 96.46%, 90.99%, 87.47% and 74.43%. Similar to the laminar flow regime experiment, a 6500 ppm non-viscoelastic PEO solution was injected (30 µL/min) resulting in Sor from pores 1 to 5 of 45.38%, 28.07%, 36.39%, 34.7% and 58.69%. Afterwards, the viscoelastic HPAM was injected (30 µL/min) resulting in final Sor from pores 1 to 5 of 48.08%, 0.00%, 17.49%, 35.30% and 8.35%. This represents an additional oil recovery of 21.95% PV which is significantly higher than at a laminar flow regime without elastic turbulence. Therefore, it can be assumed that the most important viscoelastic recovery mechanism is the elastic turbulence. It has to be noted that elastic turbulence is usually observed at shear rates which are several times higher than those encountered in the reservoir. Therefore, although the oil recovery is significantly higher for elastic turbulence, it is not applicable in the field yet. Here, viscoelastic polymer solutions have to be developed which show a remarkable earlier onset of elastic turbulence. The elastic turbulence characteristics responsible for the high additional oil recovery can be seen in Figure 22 and can be summarized as streamline crossing, fluctuation/stream curvature of the main stream and penetration of the stream into small corners of the grains. Although the results of this work show promising insights, it has to be seen critically. The shear rates required to see elastic turbulence are significantly higher than observed in the reservoir. In the 1 results presented in Figure 22, the shear rate is approximately 1300 s− , which is about 10 (in the near-wellbore region) to 1000 times (deep in the reservoir) higher than in the reservoir. Therefore, results shown here are not transferable to a realistic field case. In contradiction to this study, Howe et al. [25] show an onset of elastic turbulence for a shear rate 1 of approximately 1–10 s− for core flooding. These rates allow for the assumption that viscoelastic oil recovery can take place at typical reservoir rates. Nevertheless, these experiments are single phase. Finally, and as a result of this study, the on-going question of this work must be: when is elastic turbulence onset really observed under reservoir conditions and in two- or even three-phase flow? If it is encountered at reservoir shear rates, viscoelasticity plays a significant role in polymer EOR, if it is not, the role of polymer viscoelasticity is strongly reduced. Polymers 2020, 12, 2276 32 of 43 Polymers 2020, 12, 2276 32 of 43

Figure 21.21. (Red)(Red) BinaryBinary imagesimages of of the the initial initial oil oil saturation saturation in in the the selected selected pores. pores. The The images images refer refer to the to evaluationthe evaluation and analysis and analysis of a 500 of ppm a 500 polymer ppm polymer solution solutionat laminar atflow laminar conditions; flow conditions; (green) Streamline (green) visualizationStreamline visualization during polyethylene during polyethylene oxide (PEO) oxide flooding (PEO) in flooding the selected in thepores. selected The pores. images The referimages to therefer evaluation to the evaluation and analysis and analysis of PEO (3350of PEO ppm) (3350 at ppm) laminar at laminar flow conditions flow conditions using an using injection an injection rate of 0.5 µL/min; (blue) Streamline visualization during 500 ppm polymer flooding in the selected pores. rate of 0.5 µL/min; (blue) Streamline visualization during 500 ppm polymer flooding in the selected The images refer to the evaluation and analysis of the 500 ppm polymer solution at laminar flow pores. The images refer to the evaluation and analysis of the 500 ppm polymer solution at laminar conditions using an injection rate of 0.5 µL/min [11]. The initial oil saturations (Soi) for pores 1 to 5 were flow conditions using an injection rate of 0.5 µL/min [11]. The initial oil saturations (Soi) for pores 1 to 97.94%, 95.21%, 90.07%, 86.18% and 84.30%. After Soi was determined, non-viscoelastic polyethylene 5 were 97.94%, 95.21%, 90.07%, 86.18% and 84.30%. After Soi was determined, non-viscoelastic oxide (PEO) were injected (0.5 µL/min) in order to displace the oil without any viscoelastic effects. polyethylene oxide (PEO) were injected (0.5 µL/min) in order to displace the oil without any The residual oil saturations (Sor) after PEO flooding from pores 1 to 5 were 97.94%, 0.00%, 90.07%, viscoelastic effects. The residual oil saturations (Sor) after PEO flooding from pores 1 to 5 were 97.94%, 34.64% and 20.18% respectively. 0.00%, 90.07%, 34.64% and 20.18% respectively.

Polymers 2020, 12, 2276 33 of 43 Polymers 2020, 12, 2276 33 of 43

FigureFigure 22.22. (Red)(Red) BinaryBinary images images of of the the initial initial oil oil saturation saturation in in the the selected selected pores. pores. The The images images refer refer to the to evaluationthe evaluation and analysis and analysis of a 500 of ppm a 500 polymer ppm polymer solution solat laminarution at flow laminar conditions; flow conditions; (green) Streamline (green) visualizationStreamline visualization during PEO during flooding PEO in the flooding selected in pores.the selected The images pores. refer The images to the evaluation refer to the and evaluation analysis ofand PEO analysis (3350 of ppm) PEO at (3350 laminar ppm) flow at laminar conditions flow using conditions an injection using ratean injection of 0.5 µ Lrate/min; of 0.5 (blue) µL/min; Streamline (blue) visualizationStreamline visualization during 500 ppm during polymer 500 ppm flooding polymer in the flooding selected in pores. the selected The images pores. refer The to images the evaluation refer to andthe evaluation analysis of and the 500analysis ppm of polymer the 500 solution ppm polymer at laminar solution flow conditionsat laminar usingflow conditions an injection using rate an of 0.5injectionµL/min rate [11 ].of The 0.5 initialµL/min oil [11]. saturations The initial were oil determined saturations for were pores determined 1 to 5 to be 93.87%, for pores 96.46%, 1 to 90.99%,5 to be 87.47%93.87%, and 96.46%, 74.43%. 90.99%, Similar 87.47% to the and laminar 74.43%. flow Similar regime to experiment, the laminar a flow 6500 regime ppm non-viscoelastic experiment, a PEO6500 µ S solutionppm non was-viscoelastic injected (30 PEOL solution/min) resulting was injected in or from (30 µL/min) pores 1 to resulting 5 of 45.38%, in Sor 28.07%, from pores 36.39%, 1 to 34.7% 5 of and45.38%, 58.69%. 28.07%, 36.39%, 34.7% and 58.69%.

A general overview and summary of viscoelasticity’s role in EOR applications is given in the 5. Polymer Viscoelasticity and Enhanced Oil Recovery: A Two-Folded Partnership next sections. As seen before, polymer viscoelasticity can have a significant impact on the polymer flooding efficiency resulting in additional oil recovered from mature fields. Assuming shear thickening not to

Polymers 2020, 12, 2276 34 of 43 be a viscosity increase, mainly the elastic turbulence flow characteristics presented in Section 3.2.3 are responsible for an incremental recovery due to viscoelasticity. Although the results presented and discussed in literature are promising, the realistic situation appears to be different as can be seen from Figure 23. When neglecting all the impacts on polymer viscoelasticity, the potential of viscoelasticity in EOR applications is remarkable. But first a decrease of viscoelasticity’s potential has to be made when taking polymer degradation into account. Mechanical, chemical, biological and thermal degradation result in a lower relaxation time of the polymer. Hence, the viscoelastic recovery mechanisms discussed in the section before are weaker. A second and actually an even more significant decrease of viscoelasticity’s importance in EOR is the result of the low shear rates observed in the reservoir. Polymers 2020, 12, 2276 34 of 43 Typically, shear rates of 1 (deep in the reservoir) to 100 s−1 (near-wellbore region) are achieved. This is too low to see flow instabilities which have been shown to be the main viscoelastic recovery mechanism.5. Polymer Viscoelasticity In order to account and Enhanced for these Oil drastic Recovery: impacts, A Two-Folded the injected Partnership polymer solution can be optimized. Nevertheless, fluid optimization with regards to chemical and biological resistance As seen before, polymer viscoelasticity can have a significant impact on the polymer flooding include the utilization of chemical agents and biocides which can cause environmental issues. efficiency resulting in additional oil recovered from mature fields. Assuming shear thickening not to In order to achieve promising results from experimental research in field applications, it is be a viscosity increase, mainly the elastic turbulence flow characteristics presented in Section 3.2.3 are absolutely necessary to improve or rather modify existing polymers. This can yield polymers that are responsible for an incremental recovery due to viscoelasticity. more resistant to the various kinds of degradation and, therefore, have a higher viscoelasticity. In Although the results presented and discussed in literature are promising, the realistic situation addition, the modification of polymer can result in polymers that show elastic turbulent flow at lower appears to be different as can be seen from Figure 23. When neglecting all the impacts on polymer shear rates and, hence, may become applicable in reservoirs. Not only the modification of existing viscoelasticity, the potential of viscoelasticity in EOR applications is remarkable. But first a decrease of but also the development of new polymer molecular structures can yield this result. viscoelasticity’s potential has to be made when taking polymer degradation into account. Mechanical, Most importantly, viscoelastic EOR mechanisms need to be further extensively investigated and chemical, biological and thermal degradation result in a lower relaxation time of the polymer. Hence, discussed in order to understand the importance of the single mechanisms. The work presented in the viscoelastic recovery mechanisms discussed in the section before are weaker. A second and actually this study indicates that elastic turbulence is the main mechanism behind viscoelastic oil recovery. an even more significant decrease of viscoelasticity’s importance in EOR is the result of the low shear Therefore, an advanced understanding of elastic turbulence, its characteristics, its triggering effects rates observed in the reservoir. as well as its contribution to oil recovery is absolutely necessary. Increase of the Viscoelastic Potential

Potential of • Pull-Out Mechanism Viscoelasticity • Stripping Mechanism in • Elastic Turbulence • EOR Improvement and  Additional Oil Recovery Modification of existing Applications Polymers • Development of new Polymers • Mechanical • Further Research on • Chemical Viscoelastic EOR • Biological Mechanisms for Advanced • Thermal Understanding Polymer Degradation

• Shear Rates are to low in the reservoir to observe flow Low Shear Rates instabilities

Lower MW Economical Constraints = Fluid Optimization Lower Viscoelasticity Mechanical: use more shear stable polymers, e.g. lower MW Chemical: use antioxidants and other Remaining Potential of stabilizing agents Viscoelasticity Biological: use biocide Thermal: use modified polymers with in EOR Applications higher thermal resistivity Addition of Antioxidants, Biocides and other Stabilizing Agents can yield to Environmental Often Increase in Mechanical Degradation Issues Figure 23. Potential and impacts on the role of polymer viscoelasticity in EOR applications. In contrast to laboratory studies, a decreasing potential is observed taking all impacts and interactions into account. Modification of existing and development of new polymers in combination with further research can drastically improve the viscoelastic influence in polymer flooding.

1 Typically, shear rates of 1 (deep in the reservoir) to 100 s− (near-wellbore region) are achieved. This is too low to see ﬂow instabilities which have been shown to be the main viscoelastic recovery mechanism. In order to account for these drastic impacts, the injected polymer solution can be optimized. Nevertheless, ﬂuid optimization with regards to chemical and biological resistance include the utilization of chemical agents and biocides which can cause environmental issues. Polymers 2020, 12, 2276 35 of 43

In order to achieve promising results from experimental research in field applications, it is absolutely necessary to improve or rather modify existing polymers. This can yield polymers that are more resistant to the various kinds of degradation and, therefore, have a higher viscoelasticity. In addition, the modification of polymer can result in polymers that show elastic turbulent flow at lower shear rates and, hence, may become applicable in reservoirs. Not only the modification of existing but also the development of new polymer molecular structures can yield this result. Most importantly, viscoelastic EOR mechanisms need to be further extensively investigated and discussed in order to understand the importance of the single mechanisms. The work presented in this study indicates that elastic turbulence is the main mechanism behind viscoelastic oil recovery. Therefore, an advanced understanding of elastic turbulence, its characteristics, its triggering effects as well as its contribution to oil recovery is absolutely necessary.

6. Summary and Conclusions In this work the role of polymer viscoelasticity was discussed in detail. A focus was given to the chemistry of viscoelastic polymers (especially HPAMs), to the physical and mathematical description of viscoelasticity itself, as well as to the viscoelastic flow phenomena including shear thinning, shear thickening and elastic turbulence. Furthermore, this study gave an extensive overview of the experimental approaches used in current and well-established literature. Experiments for quantitative and qualitative evaluation of polymer viscoelasticity were presented. Additionally, this work gave an in-depth overview of the different impacts on the polymer’s viscoelasticity in EOR applications as well as of the different types of degradation a polymer encounters in the reservoir. Finally, this study extensively discusses the viscoelasticity-related oil-recovery mechanisms underlining the significant importance of elastic turbulence. Structurally speaking, the chemistry of viscoelastic polymers such as HPAM can strongly vary and allows a large number of molecule modifications. Strong impacts on viscoelasticity are observed from high salinities, mechanical, thermal, chemical and biological degradation. EOR polymer solutions require the performance of fluid optimization in terms of concentration and molecular weight. Viscoelastic flow phenomena encountered in porous media, e.g., sandstones, are shear thinning, shear thickening and have elastic turbulence, whereas shear thickening is not a viscosity increase, but an additional pressure drop. Viscoelasticity-related recovery mechanisms can be summarized as a pulling and stripping mechanism, oil-thread flow and elastic turbulence. Regarding the dominance of mechanisms, shear thickening is not a viscosity increase as indicated by the apparent viscosity measurements, but an additional pressure drop caused by elastic turbulence. Elastic turbulence is assumed to have the most significant effect on additional oil recovery as was shown by two-phase experiments. This is summarized as changing stream width, changing stream direction, and penetration of the stream into small corners, build-up and immediate collapse of vortices and streamline crossing. Overall, we present a good justification for the potential or limits of polymer viscoelasticity on oil recovery. The industry is highly divided on the interpretations of the data concerning viscoelasticity. From the operational point of view these appear challenging and unclear, whereas they are much easier to digest from the laboratory side. Further studies continue suggesting mixed data on the effect on oil recovery or the reduction on residual oil saturation due to the use of polymers.

Author Contributions: A.R. worked on conceptualization and wrote initial draft. R.E.H. proofed on conceptualization and results validation, M.T. and N.L. worked on data analysis and draft editing, L.G. reviewed and produced the final version. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: We acknowledge support by Open Access Publishing Fund of Clausthal University of Technology. Conflicts of Interest: The authors declare no conflict of interest. Polymers 2020, 12, 2276 36 of 43

Abbreviations and Symbols

AMPS 2-acrylamide-2-methyl CaBER Capillary break-up extensional rheometer CT Computer tomography DLS Dynamic light scattering EOR Enhanced oil recovery eVROC Extensional viscometer-rheometer-on-a-chip FiSER Filament stretching extensional rheometer GSG Glass-Silicon-Glass HPAM Hydrolyzed polyacrylamide ODES-DOS Optically-detected elastocapillary self-thinning dripping-onto-substract PAM Polyacrylamide PEO Polyethylene oxide PTFE Polytetrafluorethane PV Pore volume RF Recovery factor ROJER Rayleigh-Ohnesorge Jet Elongational Rheometer SRB Sulphate-reducing bacteria B Deformation tensor [-] 1 γ Shear rate [s− ] 1 γoverlap Overlap shear rate G’ vs. G” [s− ] De Deborah number [-] Dp Mean grain diameter [m] Dparticle Particle diameter [m] 3 δfluid Fluid density [kg/m ] 3 δparticle Particle density [kg/m ] ∆p Differential pressure [Pa] ε Porosity [-] f 1 Particle fraction [-] ϕ1,2 Time derivates [-] g Gravitational acceleration [m/s2] G Relaxation modulus [Pa.s] G’ Storage modulus [Pa.s] G” Loss modulus [Pa.s] Hmicro Microchannel height [m] 2 kwater Relative water permeability [m ] L Flow length [m] Lmicro Microchannel length [m] λ Relaxation time [s] Mw Molecular weight [MDa] Mw, max Maximum molecular weight [MDa] µ Viscosity [Pa.s] µapp Apparent viscosity [Pa.s] µdynamic Dynamic viscosity [Pa.s] N1,2 Normal stress difference [Pa] η Shear viscosity [Pa.s] Q Flow rate [m3/s] Rem Modified Reynolds number [-] Soi Initial oil saturation [-] Sor Residual oil saturation [-] σxx Normal stress in x-direction [Pa] σyy Normal stress in y-direction [Pa] t Time [s] Polymers 2020, 12, 2276 37 of 43

τ Shear stress [Pa] vs Superﬁcial velocity [m/s] vsettlement Particle settlement velocity [m/s] ν Elastic stress [Pa] Wi Weissenberg number [-]

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